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Version 1.0 (7/2012) -View slide shows and more
here
Access the
head menu by hitting the F1 or F2 or … key on the Calculator. To
access an item, simply scroll down from the head menu using the
cursor buttons.
The following
gives an overview of all functions in the
Main module:
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F1:
Limits
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F2:
Derivatives
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F3:
Integrals
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F4: Trig+Tools
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F5: Calculus+
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F6:
Physics Applications (stepwise) |
F7:
Exit
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1
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Rules
on Limits
incl: L'hopital, rational
functions
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Find
Derivatives
incl. by Def., Secant-TangentLine
Animation
, Relative Rate of Change, Evaluate f',
Find and Evaluate f''
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Find
Antiderivatives
of f(x)
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UnitCircle
Click
here for details
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Functions |
Hydrostatic Force |
Exit
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2
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Find
1-sided Limit
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Show
Steps for Chain-, Product-, Quotient- and Power Rule. Or
using the Definition.
View
Sample
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Show
Steps for Definite Integrals, Integration
by U-Substitution, by Parts,
by Partial Fractions, Expand&Integrate,
Rewrite&Integrate,
ArcTan(x) Integrals,
ArcSin(x) Integrals,
Power Rule.
Weierstrass Substitution,
View
Sample |
List
of
Trig-Identities
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Calculus
BC or Calculus II
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Work =
∫Force |
About
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3
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Find
Limit
of f(x) as x-> a
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Rules
to Find f':
Product-, Quotient-, Chain-, Trig-deriv.
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Rules
to Integrate
incl Integration by Subst., by
parts, power rule, Trig, FTC
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List
of
Derivatives and Integrals of Trig Functions
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Multivar. calculus
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Fluid
Force |
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4
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L'Hopital Rule - Step by Step |
Make
SignChart of f(x), f'(x) and f''(x)
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Net
Area
∫ f(x)dx
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Ln(x)
- Rules
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Area Approximation |
Mass of
Center |
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5
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Continuity
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Find
Rel Min/Max
when is f'(x)=0
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f(a)=f(x0)+∫f'(x)dx |
Find
Intersection
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Differential Equations |
Moments
of Inertia |
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6
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Continuity
Solver
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Find
Tangent Line
of f(x) at x=a
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Total
Area
∫|f(x)|dx
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Solver |
Implicit Differentiation |
Radius
of Gyration |
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7
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Continuity/ Differentiability Checker
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Find
Point of Tangency
of f(x) and a linear function
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Enclosed
Area
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Factor |
Param, Vector, Polar |
Heat
Transfer |
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8
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Intermediate
Value Theorem
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Parallel
Tangents |
Average
Value Theorem
of f(x) on [a,b]
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Expand |
Related
Rates |
Unit
Converter |
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9
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Find
Normal Line
of f(x) at x=a
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Area
Approximation
Click here for details
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Synthetic Division in steps |
Sequences and Series |
Exponents and Logarithms |
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A
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Differential
Equations
Click here for details
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Find
Volume
Click here for details
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Partial
Fractions in steps. |
Volume of Solids |
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B
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Implicit
Differentiation
Click here for details
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Common
Denominator |
Rate
Problems (Water or Oil leaking, Cars, Amusement Park, etc) |
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C
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Average
Rate of Change |
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Simplify Fractions |
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D
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Find
Secant Line |
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Newton
Method
to
estimate zeros |
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E
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Mean Value Theorem
Find c on [a,b], so that f'(c)=[f(b)-f(a)]/(b-a)
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Bisection Method
to
estimate zeros |
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F |
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Find Inverse Slope
Compute d/dx[f-1(c)]
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Rad->Deg |
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G |
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1-dim. Motion
Click here for details
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Deg ->
Rad |
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H |
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Related Rates
Intro, Examples and Animations
(Pond Surface expands, Moving Ladder) |
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I |
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Piecewise defined Functions
Compute a and b so that f(x) is
continuous and differentiable
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J |
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Logarithmic Differentiation |
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K |
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Differentials |
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L |
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Function
module (stepwise solutions) :
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F1: Functions
f(x)
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All in
1 Explorer |
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Graph f(x)
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Find f(g(x)
in steps
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Find
Inverse
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Find
Asymptotes
vertical and horizontal
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Slant
Asymptotes
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Find Domain |
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Find
Discontinuity
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Find Range
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Find Symmetry
even, odd, neither
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Find Zeros
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Find Rel Min/Max
when f'(x)=0
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Find Absolute Minimum and Maximum
of f(x) on [a,b]
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Find Inflection Points
of f(x) on [a,b]
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2.2
The Differential Equations Module
The following
gives an overview of all functions in the Differential Equations
module:
DIFFERENTIAL
EQUATIONS
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Option#
in head menu
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F1:
Enter DEQ
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F2:
Solve DEQ
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F3:
Steps |
F4:
Compute
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F5:
Graph
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F6:
Euler
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F6:
Exit
Return
to main screen)
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1
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dy/dx
= f(x,y)
Any
separable Diff Eqn.
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Solve
dy/dx
= f(x,y)
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Show
Steps |
Compute
y(a)
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Graph
Slope Field
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Approximate
analyt. solution to Diff Eqn. upon entering (x0,y0),
step size and #points.
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2
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y'(t)
= k*y(t)
Exponential Growth
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Solve
y'(t)
= k*y(t)
Exponential Growth
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Solve
y(x)=C
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Graph
Particular Solution
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3
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y'(t)
= k*(y(t)-A)
Ex: Newton's Law of Cooling
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Solve
y'(t)
= k*(y(t)-A)
Ex: Newton's Law of Cooling
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Tangent
at x=a
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Clear
Graph
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4
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y'(t)
= k*(A-y(t))
Ex: Wolves problem
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Solve
y'(t)
= k*(A-y(t))
Ex: Wolves problem
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Find d2y/dx2
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Select
Window Size
define xmin, xmax, ymin, ymax, #
vertical and horiz. lines
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5
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y'(t)
= k*y*(A-y)
Logistic Growth
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Solve
y'(t)
= k*y*(A-y)
Logistic Growth
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Limit
x-> infinity
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2.3
The Implicitly Defined Functions & Implicit
Differentiation Module
The
following gives an overview of all functions in the Implicitly
Defined Functions & Implicit Differentiation Module:
IMPLICITLY
DEFINED FUNCTIONS & IMPLICIT DIFFERENTIATION
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Option#
in head menu
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F1:
Enter Equation
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F2:
Graph Equation
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F3:
(x,y) |
F4:
dy/dx
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F5:
d2y/dx2
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F6:
Tangents
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F7:
Exit
Return
to main screen
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1
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Ex1)
x2+y2=4 or
Ex2) y3 + 3x2y + 13 = 0
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Find
y given x. |
Find
dy/dx
Ex1) y'=-x/y
Ex2) y'=(-2xy)/(x2+y2)
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Find
d2y/dx2
Ex1) y"=-(x2+y2)/y3
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Find
Tangent at x=a
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2
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Find
x given y. |
Compute
Slope at (x,y)
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Compute
Concavity
at (x,y)
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Find
Tangent at y=c
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3
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Show Steps
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Show Steps
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Find
Horizontal Tangents (dy/dx = 0)
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4
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Find
Vertical Tangents (dx/dy = 0)
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2.4
The 1-Dimensional Motion Module
The following
gives an overview of all functions in the 1-Dimensional Motion
Module:
1-DIMENSIONAL MOTION
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Option#
in head menu
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F1:
Rules
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F2:
Velocity
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F3:
Acceleration
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F4:
Exit
Return
to main screen
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1
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Ex1)
v(t)=s'(t)
Ex2) speed increases if v(t) and a(t) are both pos. or neg.
Ex3) Object reverses when v(t) changes sign.
And more.
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Animation:
Vertical Ball Throw -
displays throw, s(t), v(t) and a(t)
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Find
Velocity Function
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2
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Speed
Definition
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Find
Position Function
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3
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Find
Average Velocity
between t1 and t2
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4
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Reverse
Direction
between t1 and t2
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5
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Total
Distance covered
between t1 and t2
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6
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Find
Position Function
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7
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Find
Acceleration Function
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2.5
The Integral Approximation Module
The following
gives an overview of all functions in the Integral
Approximation Module:
INTEGRAL APPROXIMATION
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Option#
in head menu
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F1:
Enter Equation
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F2:
Approximate
Each Method below involves
numerical answers and graphical explanations.
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F3:
Exact Answer for comparison
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F4:
Exit
Return
to main screen
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1
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Enter f(x), a, b, and #subintervals
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LRAM
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2
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MRAM
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3
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RRAM
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4
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Trapezoids
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5
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Area
Approximation
using data from table.
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6 |
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Approximation
Rules |
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7 |
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Simpson
Rule |
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2.6
The Volume Module
The following
gives an overview of all functions in the Volume Module:
VOLUME
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Option#
in head menu
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F1:
Disk Method
about x-axis
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F2:
Washer Method
about x-axis
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F3:
Cross Sections
Displays
the formulas and computes volumes of solids having
various cross sections.
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F4:
Shell Method
about y-axis
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F5:
Washer Method
about y-axis
Enter
R(y), r(y) and [c,d]
to compute Volume of enclosed
rotated area about y-axis
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F6: Exit
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1
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Enter
R(x) and [a,b]
to compute Volume of rotated area
about x-axis
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Enter
R(x), r(x) and [a,b]
to compute Volume of enclosed
rotated area about x-axis
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Enter
H(x), h(x) and [a,b]
to compute Volume of enclosed
rotated area about y-axis
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2
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2
Equal Volumes
Find k on (a,b) so that
Volume1=Volume2
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2
Equal Volumes
Find k on (a,b) so that
Volume1=Volume2
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2
Equal Volumes
Find k on (a,b) so that
Volume1=Volume2
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3
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Rotate
about the horizontal line y=h
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Rotate
about the vertical line x=a
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4
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2.7
The Unit Circle Module
The following
gives an overview of all functions in the Unit Circle Module:
UNIT
CIRCLE
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F1:
Quadrant I
Display
of Unit Circle Coordinates for 0, 30, 45, 60 degrees.
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F2:
Quadrant II
Display
of Unit Circle Coordinates for p0, 120, 135, 150 degrees.
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F3:
Quadrant III
Display
of Unit Circle Coordinates for 180, 210, 225, 240 degrees.
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F4:
Quadrant IV
Display
of Unit Circle Coordinates for 270, 300, 315, 330 degrees.
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F5:
Rules
Incl:
Circle Equation, sin(x), cos(x) , tan(x).
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F6:
Exit
Return
to main screen
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2.8
The AP Calculus (BC) Module
The following
gives an overview of all functions in the AP Calculus (BC) Module:
AP CALCULUS (BC)
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Option#
in head menu
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F1:
Integrals
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F2:
Parametrics
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F3:
Vectors
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F4:
Polar
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F5:
Series
Click
here for details
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F6:
Exit
Return
to main screen
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1
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Improper
Integrals
|
Evaluate
(x(t),y(t))
at t=a |
Vector
rules such as addition,
multiplication, etc.
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Conversion:
Rectangular <-> Polar
Coordinates
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2
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Integration
by Trig Substitution
(I)
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Graph
Curve (x(t),y(t)) on [t1,t2]
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Example:
computation of new plane speed and
direction.
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Intersection |
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3
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Integration by Trig Substitution
(II)
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Find
dy/dx
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Graph
Curve (x(t),y(t)) on [t1,t2]
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Graph
Polar Curve
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4
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Curve
Length of f(x) on [a,b]
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Find
Tangent Line at t=a
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When
entering Position function s(t),
compute
of v(t), a(t), evaluate them , speed and magnitude of a(t)
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Find
x-axis, y-axis or origin
Symmetry
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5
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Center
of Mass
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Find
Horizontal Tangents
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When
entering Velocity function v(t),
compute
of s(t), a(t), evaluate them, speed and magnitude of a(t)
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Find
dy/dx
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6
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Surface Area(x)
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Find
Vertical Tangents
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When
entering Acceleration function a(t),
compute
of s(t), v(t), evaluate them, speed and magnitude of a(t)
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Find
Tangents
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7
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Surface Area(y)
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Find
d2y/dx2
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Gradient
(2-dim)
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Compute
Area between origin and curve
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8
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Find
Curve Length of (x(t),y(t))
on [t1,t2]
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Direct.
Derivative (2-dim)
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Compute
Enclosed Area
between R(phi) and r(phi).
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9
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Find
Enclosed Area of loops
on [t1,t2]
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Curl
(3-dim) |
Find
Angle theta given x and r(theta)
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A
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Find
Surface Area of (x(t),y(t))
on [t1,t2]
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Divergence
(3-dim) |
Find
Angle theta given y and r(theta) |
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B
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Find
Volume of Solid of Revolution on
[t1,t2]
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Compute
Curve
Length of r(phi) on [phi1,phi2]
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2.9
The Series and Convergence Module
The following
gives an overview of all functions in the Series and
Convergence Module:
SERIES
& CONVERGENCE
|
Option#
in head menu
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F1:
Enter Series
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F2:
Tests for Convergence
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F3:
Power Series
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F4:
Taylor Series
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F5:
Error |
F6:
Exit
Return
to Calculus (BC)
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1
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Find
terms of a Recursive Sequence:
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Enter
Equation
of Series |
Find
Interval of Convergence of a Power Series using Ratio Test.
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Graph
f(x) and its power series representation
about x=a using n Terms.
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Alt
Series
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2
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Find
terms of an Explicit Sequence: |
N-th
Term Test for Convergence
Does an --> 0 as
n--> oo ?
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Find
Taylor Series Representation of
f(x) about x=a using n Terms.
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Alt
Series: Find n. |
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3
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Sequence Convergence Tester: |
Geometric
Series Test
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Find
Taylor Series about x=a using its definition. Use
it to approx. f(x) near x=a. Also differentiate and
integrate it.
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Alt
Taylor Series |
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4
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Sequence
Formula Finder:
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Integral
Test
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Differentiate
Taylor series of f(x)
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Taylor
Series for f(x) |
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5
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Partial
Sum:
Sum Up the
first n Terms
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Alternating
Series Test
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Integrate
Taylor series of f(x)
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Taylor
Series |f^(n+1)(x)|<M |
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6
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Graph
the first n Terms of Series
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Ratio
Test
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Taylor
Series: Find n. |
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7
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All-in-One-Tester
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8
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Comparison
Test
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9
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Limit
Convergence Test |
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A
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p-Series
Test |
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B |
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Root
Test |
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C |
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Find
Sum |
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2.10
Calculus III
The following
gives an overview of all functions in the Calculus III Module:
CALCULUS
III
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F1:
Plot f(x,y)
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F2:
Limits
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F3:
Differentiate
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F4:
Integrate
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F5:
More
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F6:
Exit |
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1
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f(x,y):
Limit
when x-> x0, y-> y0 |
f(x,y)
Find and Evaluate
fx,
fy, fxx, fxy, fyx, fyy
|
int(int(
f(x,y) ))
Indefinite, double Integral |
LaPlace
Transform |
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2
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f(x,y,z):
Limit
when x-> x0, y-> y0 , z->
z0 |
f(x,y)
Find Rel. Extrema
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int(int(
f(x,y) ))
with xmin, xmax, ymin and ymax
as integration bounds
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Fourier
Transform |
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3
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Directional Derivative - multidimensional |
int(int(
f(x,y) ))
with xmin, xmax, g1(x) and g2(x)
or ymin, ymax, h1(y) and h2(y)
as integration bounds |
Gamma
Function |
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4
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Find
Differential (2-variables) |
int(int(int(
1dzdydx )))
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Bessel
Function |
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5
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f(x(t),y(t))
Find
and Evaluate f'(x(t),y(t)) |
int(int(int(
f(x,y,z) dzdydx ))) |
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6
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f(x,y,z)
- Gradient
Find and Evaluate fx, fy, fz.
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7
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Find
Differential (3-variables) |
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8
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f(x(t),y(t),z(t))
Find
and Evaluate f'(x(t),y(t),z(t))
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9 |
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Implicit
Differentiation: F(x,y) = 0
Find dy/dx |
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A |
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Implicit
Differentiation: F(x,y,z)=0
Find dz/dx, Find dz/dy
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B |
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Find
Tangent plane
at (x0,y0,z0) when F(x,y,z)=0.
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C |
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Jacobian
Matrix-
multidimensional |
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D |
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Hesse
Matrix-
multidimensional |
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E |
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Lagrange Multiplier-
multidimensional |
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F |
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Taylor
Series - multidimensional |
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Module: Exponential &
Logarithmic Functions
| |
F1: Rules |
F2:
Functions |
F3: Solver |
F4: Exit |
| 1 |
e=limit(1+1/n)^n |
Exponential |
Exponential Growth |
Exit |
| 2 |
Exponents |
Logarithmic |
Money-Growth |
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| 3 |
Logarithms |
Find a,b in
y=a*b^x |
Effective Interest
Rate |
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| 4 |
Log: Compress |
Standard Normal
Curve |
Logarithm Solver |
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| 5 |
Log: Expand |
Logistic Curve |
Evaluate
logb(N) |
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| 6 |
Rewrite Log_b(y)=x
as y=b^x |
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Solve any Equation |
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| 7 |
Rule 72 |
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| 8 |
Change of base |
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