Business Calculus TI89 App with Step by Step Solutions

Solve Business Calculus questions stepwise using the TI89 Calculator


Scroll down to select APP and observe the provided
Step by Step solutions to the right. It is worldwide
the only Math software that can do this!!!   

View Calculus Made Easy - Slide Show

Click to view the Differentiation and Integration slides at your speed.

Click to Bookmark This Page

 

 

 
 
     

Version 2.0

-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: 

 

F1: Limits

F2: Derivatives

F3: Integrals

F4: Trig+Tools

F5:  Calculus+

F6: Business Calculus (stepwise)

F7: Exit

1

Rules on Limits
incl: L'hopital, rational functions

Find Derivatives
incl. by Def., Secant-TangentLine
Animati
on , Relative Rate of Change, Evaluate f', Find and Evaluate f''

Find Antiderivatives
of f(x)
 

UnitCircle
Click here for details

Functions

Maximize Revenue/Profit

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

 Calculus BC or Calculus II

Marginal Analysis

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

Multivar. calculus Demand Analysis  

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

Area Approximation Find dp/dt , dq/dt  

5

 Continuity

Find Rel Min/Max
when is f'(x)=0
f(a)=f(x0)+∫f'(x)dx  Find Intersection    Differential Equations Economic Order Quantity  

6

 Continuity Solver

Find Tangent Line
of f(x) at x=a

Total Area
|f(x)|dx

Solver Implicit Differentiation Price Elasticity  

7

Continuity/ Differentiability Checker

Find Point of Tangency
of f(x) and a linear function

Enclosed Area

Factor Param, Vector, Polar Simplex Algorithm  

8

Intermediate Value Theorem 

Parallel Tangents

Average Value Theorem
of f(x) on [a,b]

Expand Related Rates ∆y=f'(x)*∆x

 

9

 

Find Normal Line
of f(x) at x=a

Area Approximation
Click here for details

Synthetic Division in steps Sequences and Series Differentials

 

A

 

Differential Equations
Click here for details

Find Volume
Click here for details

Partial Fractions in steps. Volume of Solids Supply Demand Analysis  

B

 

Implicit Differentiation
Click here for details

  Common Denominator Rate Problems (Water or Oil leaking, Cars, Amusement Park, etc) Consumer Surplus  

C

  Average Rate of Change   Simplify Fractions   Compound Interest  

D

  Find Secant Line   Newton Method 
to estimate zeros
  Effective Interest Rate  

E

  Mean Value Theorem
Find c on [a,b], so that f'(c)=[f(b)-f(a)]/(b-a)
  Bisection Method 
to estimate zeros
  Exponents and Logarithms  

F

  Find Inverse Slope
Compute d/dx[f-1(c)]
  Rad->Deg   Logistics Models  

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

Option# in head menu

F1: Disk Method 
about x-axis

F2: Washer Method
about x-axis

F3: Cross Sections

Displays the formulas and computes  volumes of solids having various cross sections. 

F4:  Shell Method
about y-axis

F5: Washer Method
about y-axis

Enter R(y), r(y) and [c,d]
to compute Volume of enclosed rotated area about y-axis 

F6: Exit

1

Enter R(x) and [a,b] 
to compute Volume of rotated area about x-axis  

Enter R(x), r(x) and [a,b]
to compute Volume of enclosed rotated area about x-axis 

Enter H(x), h(x) and [a,b] 
to compute Volume of enclosed rotated area about y-axis 

 

2

2 Equal Volumes
Find k on (a,b) so that Volume1=Volume2

2 Equal Volumes
Find k on (a,b) so that Volume1=Volume2

 

2 Equal Volumes
Find k on (a,b) so that Volume1=Volume2

 

 

3

 

Rotate about the horizontal line y=h

 

Rotate about the vertical line x=a

 

 

4

 

 

 

 

 

 

 

 


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)|<M  

6

Graph  the first n Terms of Series

Ratio Test  

 

 

Taylor Series: Find n.   

7

 

All-in-One-Tester

       

8

  Comparison Test          

9

  Limit Convergence Test        

A

  p-Series Test         

B

  Root Test        

C

  Find Sum        

 

 

 

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