# Calculus with Physics Applications TI89 App with Step by Step Solutions

## Solve Calculus with Physics questions stepwise using the TI89 Calculator

Version 1.0 (7/2012)

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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:

 F1: Limits F2: Derivatives F3: Integrals F4: Trig+Tools F5:  Calculus+ F6: Physics Applications (stepwise) F7: Exit 1 Rules on Limits incl: L'hopital, rational functions Find Derivatives incl. by Def., Secant-TangentLine Animation , Relative Rate of Change, Evaluate f', Find and Evaluate f'' Find Antiderivatives of f(x) UnitCircle Click here for details Hydrostatic Force Exit 2 Find 1-sided Limit Show Steps for Chain-, Product-, Quotient- and Power Rule. Or using the Definition.    View Sample 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 Work = ∫Force About 3 Find Limit of f(x) as x-> a Rules to Find f': Product-, Quotient-, Chain-, Trig-deriv. Rules to Integrate incl Integration by Subst., by parts, power rule, Trig, FTC List of Derivatives and Integrals of Trig Functions Fluid Force 4 L'Hopital Rule - Step by Step Make SignChart of  f(x), f'(x) and f''(x) Net Area  ∫ f(x)dx Ln(x) - Rules Mass of Center 5 Continuity Find Rel Min/Max when is f'(x)=0 f(a)=f(x0)+∫f'(x)dx Find Intersection Moments of Inertia 6 Continuity Solver Find Tangent Line of f(x) at x=a Total Area ∫|f(x)|dx Solver Radius of Gyration 7 Continuity/ Differentiability Checker Find Point of Tangency of f(x) and a linear function Enclosed Area Factor Heat Transfer 8 Intermediate Value Theorem Parallel Tangents Average Value Theorem of f(x) on [a,b] Expand Related Rates Unit Converter 9 Find Normal Line of f(x) at x=a Synthetic Division in steps A Partial Fractions in steps. B Common Denominator Rate Problems (Water or Oil leaking, Cars, Amusement Park, etc) C Average Rate of Change Simplify Fractions D Find Secant Line Newton Method  to estimate zeros E Mean Value Theorem Find c on [a,b], so that f'(c)=[f(b)-f(a)]/(b-a) Bisection Method  to estimate zeros F Find Inverse Slope Compute d/dx[f-1(c)] Rad->Deg G 1-dim. Motion Click here for details Deg -> Rad H Related Rates Intro, Examples and Animations (Pond Surface expands, Moving Ladder) I Piecewise defined Functions Compute a and b so that f(x) is continuous and differentiable J Logarithmic Differentiation K Differentials L

Function module (stepwise solutions) :

 F1: Functions           f(x) All in 1 Explorer Graph f(x) Find f(g(x) in steps Find Inverse Find Asymptotes  vertical and horizontal Slant Asymptotes Find Domain Find Discontinuity Find Range Find Symmetry even, odd, neither Find Zeros Find Rel Min/Max when f'(x)=0 Find Absolute Minimum and  Maximum of f(x) on [a,b] Find Inflection Points of f(x) on [a,b]

2.2  The Differential Equations Module

The following gives an overview of all functions in the Differential Equations module:

DIFFERENTIAL EQUATIONS

 Option# in head menu F1: Enter DEQ F2: Solve DEQ F3: Steps F4: Compute F5: Graph F6: Euler F6: Exit Return to main screen) 1 dy/dx = f(x,y)   Any separable Diff Eqn. Solve dy/dx = f(x,y) Show Steps Compute y(a) Graph Slope Field Approximate analyt. solution to Diff Eqn.  upon entering (x0,y0), step size and #points. 2 y'(t) = k*y(t) Exponential Growth Solve  y'(t) = k*y(t) Exponential Growth Solve y(x)=C Graph Particular Solution 3 y'(t) = k*(y(t)-A) Ex: Newton's Law of Cooling Solve y'(t) = k*(y(t)-A) Ex: Newton's Law of Cooling Tangent at x=a Clear Graph 4 y'(t) = k*(A-y(t)) Ex: Wolves problem Solve y'(t) = k*(A-y(t)) Ex: Wolves problem Find d2y/dx2 Select Window Size define xmin, xmax, ymin, ymax, # vertical and horiz. lines 5 y'(t) = k*y*(A-y) Logistic Growth Solve y'(t) = k*y*(A-y) Logistic Growth Limit x-> infinity

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

 Option# in head menu F1: Enter Equation F2: Graph Equation F3:  (x,y) F4:  dy/dx F5: d2y/dx2 F6: Tangents F7: Exit Return to main screen 1 Ex1) x2+y2=4 or  Ex2) y3 + 3x2y + 13 = 0 Find y given x. Find dy/dx Ex1) y'=-x/y Ex2) y'=(-2xy)/(x2+y2) Find d2y/dx2 Ex1) y"=-(x2+y2)/y3 Find Tangent at x=a 2 Find x given y. Compute  Slope at (x,y) Compute  Concavity at (x,y) Find Tangent at y=c 3 Show Steps Show Steps Find Horizontal Tangents (dy/dx = 0) 4 Find Vertical Tangents (dx/dy = 0)

2.4  The 1-Dimensional Motion Module

The following gives an overview of all functions in the 1-Dimensional Motion Module:

1-DIMENSIONAL MOTION

 Option# in head menu F1: Rules F2: Velocity F3: Acceleration F4: Exit   Return to main screen 1 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. Animation: Vertical Ball Throw -  displays throw, s(t), v(t) and a(t) Find Velocity Function 2 Speed Definition Find Position Function 3 Find Average Velocity  between t1 and t2 4 Reverse Direction   between t1 and t2 5 Total Distance covered between t1 and t2 6 Find Position Function 7 Find Acceleration Function

2.5  The Integral Approximation Module

The following gives an overview of all functions in the Integral Approximation Module:

INTEGRAL APPROXIMATION

 Option# in head menu F1: Enter Equation F2: Approximate Each Method below involves numerical answers and graphical explanations. F3: Exact Answer for comparison F4: Exit Return to main screen 1 Enter f(x), a, b, and #subintervals LRAM 2 MRAM 3 RRAM 4 Trapezoids 5 Area Approximation using data from table. 6 Approximation Rules 7 Simpson Rule

2.6  The Volume Module

The following gives an overview of all functions in the Volume Module:

VOLUME

2.7  The Unit Circle Module

The following gives an overview of all functions in the Unit Circle Module:

UNIT CIRCLE

 F1: Quadrant I Display of Unit Circle Coordinates for 0, 30, 45, 60 degrees. F2: Quadrant II Display of Unit Circle Coordinates for p0, 120, 135, 150 degrees. F3: Quadrant III Display of Unit Circle Coordinates for 180, 210, 225, 240 degrees. F4: Quadrant IV Display of Unit Circle Coordinates for 270, 300, 315, 330 degrees. F5: Rules Incl: Circle Equation, sin(x), cos(x) , tan(x). F6: Exit   Return to main screen

2.8  The AP Calculus (BC) Module

The following gives an overview of all functions in the AP Calculus (BC) Module:

AP CALCULUS (BC)

 Option# in head menu F1: Integrals F2: Parametrics F3: Vectors F4: Polar F5: Series Click here for details F6: Exit   Return to main screen 1 Improper Integrals Evaluate (x(t),y(t)) at  t=a Vector rules such as addition, multiplication, etc. Conversion: Rectangular <-> Polar Coordinates 2 Integration by Trig Substitution (I) Graph Curve (x(t),y(t)) on [t1,t2] Example: computation of new plane speed and direction. Intersection 3 Integration by Trig Substitution (II) Find dy/dx Graph Curve (x(t),y(t)) on [t1,t2] Graph Polar Curve 4 Curve Length of f(x) on [a,b] Find Tangent Line at t=a When entering Position function s(t),  compute of v(t), a(t), evaluate them , speed and magnitude of a(t) Find x-axis, y-axis or origin Symmetry 5 Center of Mass Find Horizontal Tangents When entering Velocity function v(t),  compute of s(t), a(t), evaluate them, speed and magnitude of a(t) Find dy/dx 6 Surface Area(x) Find Vertical Tangents When entering Acceleration function a(t), compute of s(t), v(t), evaluate them, speed and magnitude of a(t) Find Tangents 7 Surface Area(y) Find d2y/dx2 Gradient (2-dim) Compute Area between origin and curve 8 Find Curve Length of (x(t),y(t)) on [t1,t2] Direct. Derivative (2-dim) Compute Enclosed Area between R(phi) and r(phi). 9 Find Enclosed Area  of loops on [t1,t2] Curl (3-dim) Find Angle theta given x and r(theta) A Find Surface Area  of (x(t),y(t)) on [t1,t2] Divergence (3-dim) Find Angle theta given y and r(theta) B Find Volume of Solid of Revolution  on [t1,t2] Compute Curve Length of r(phi) on [phi1,phi2]

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 F1: Enter Series F2: Tests for Convergence F3: Power Series F4: Taylor Series F5: Error F6: Exit Return to Calculus (BC) 1 Find terms of a Recursive  Sequence: Enter Equation of Series Find Interval of Convergence of a Power Series using Ratio Test. Graph f(x) and its power series representation about x=a using n Terms. Alt Series 2 Find terms of an Explicit  Sequence: N-th Term Test for Convergence Does an --> 0 as n--> oo ? Find Taylor Series Representation of f(x) about x=a using n Terms. Alt Series: Find n. 3 Sequence Convergence Tester: Geometric Series Test Find Taylor Series about x=a using its definition. Use it to approx. f(x) near x=a. Also differentiate and integrate it. Alt Taylor Series 4 Sequence Formula Finder: Integral Test Differentiate Taylor series of f(x) Taylor Series for f(x) 5 Partial Sum: Sum Up the first n Terms Alternating Series Test Integrate Taylor series of f(x) Taylor Series |f^(n+1)(x)|

2.10  Calculus III

The following gives an overview of all functions in the Calculus III Module:

CALCULUS III

 F1: Plot f(x,y) F2: Limits F3: Differentiate F4: Integrate F5: More F6: Exit 1 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 2 f(x,y,z): Limit  when x-> x0, y-> y0 , z-> z0 f(x,y)  Find Rel. Extrema int(int( f(x,y) )) with xmin, xmax, ymin and ymax  as integration bounds Fourier Transform 3 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 4 Find Differential (2-variables) int(int(int( 1dzdydx ))) Bessel Function 5 f(x(t),y(t))  Find and Evaluate  f'(x(t),y(t)) int(int(int( f(x,y,z) dzdydx ))) 6 f(x,y,z) - Gradient   Find and Evaluate  fx, fy, fz. 7 Find Differential (3-variables) 8 f(x(t),y(t),z(t)) Find and Evaluate  f'(x(t),y(t),z(t)) 9 Implicit Differentiation: F(x,y) = 0 Find dy/dx A Implicit Differentiation: F(x,y,z)=0  Find dz/dx, Find dz/dy B Find Tangent plane   at (x0,y0,z0) when F(x,y,z)=0. C Jacobian Matrix- multidimensional D Hesse Matrix- multidimensional E Lagrange Multiplier- multidimensional F Taylor Series - multidimensional

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 3 Logarithms Find a,b in y=a*b^x Effective Interest Rate 4 Log: Compress Standard Normal Curve Logarithm Solver 5 Log: Expand Logistic Curve Evaluate logb(N) 6 Rewrite Log_b(y)=x as y=b^x Solve any Equation 7 Rule 72 8 Change of base