TI-84 Graphing Calculator Guide designed to accompany

64 Pages·2011·0.78 MB·English

TI-84 Graphing Calculator Guide designed to accompany

Calculus Concepts: An Informal Approach to the Mathematics of Change 5e

Preliminaries 1
0.1 Setup and Calculations 1
0.1.0 Turning the Calculator ON or OFF 1
0.1.1 Settings 1
0.1.1a Mode 1
0.1.1b Statistical Setup 1
0.1.1c Graphing Window Format 2
0.1.2 Calculating 2
0.1.3 Accessing 2ND and ALPHA Functions 3
0.1.4 Using ENTRY and ANS to Reuse Expressions 4
0.1.5 Storing and Recalling Values 4
Chapter 1 Ingredients of Change: Functions and Limits 5
1.1 Functions: Four Representations 5
1.1.1 Entering a Function into Y1 5
1.1.2 Evaluating a Function that is in Y1 5
1.1.2a Changing the number of decimal places reported by the calculator 6
1.1.2b Re-evaluating a previous entry 6
1.1.2c Editing a previous entry 6
1.1.3 Using Equation Solver 6
1.1.4 Graphing a Function 7
1.2 Function Behavior and End Behavior Limits 9
1.2.1 Investigating End Behavior 9
1.2.1a Graphically investigating end behavior 9
1.2.1b Numerically investigating end behavior 9
1.3 Limits and Continuity 10
1.3.1 Numerically Investigating Function Behavior 10
1.3.2 Graphing a Piecewise Defined Function 10
1.4 Linear Functions and Models 11
1.4.1 Entering Data 11
1.4.2 Graphing a Scatter Plot 12
1.4.2a Setting up STAT PLOT 12
1.4.2b Viewing a scatter plot 12
1.4.3 Calculating First Differences 12
1.4.4 Fitting a Linear Model to Data 14
1.4.5 Aligning Data 15
1.4.6 Using Unrounded Models in Y1 16
1.4.7 Restoring a Missing Column on the List Screen 16
1.5 Exponential Functions and Models 17
1.5.1 Calculating Percentage Changes 17
1.5.2 Calculating Percentage Changes for Data 18
1.5.3 Fitting an Exponential Model to Data 18
1.6 Models in Finance 19
1.6.1 Evaluating a Loan with Simple Interest 19
1.6.2 Evaluating a Loan with Compound Interest 19
1.6.3 Calculating Doubling Time 20
1.7 Constructed Functions 22
1.7.1 Constructing a Function Using Multiplication 22
1.7.2 Constructing a Function Using Composition 23
1.7.3 Approximating the Model of an Inverse Function 24
1.8 Logarithmic Functions and Models 25
1.8.1 Fitting a Logarithmic Model 25
1.8.2 Fitting the Inverse of a Log Model 25
1.9 Quadratic Functions and Models 27
1.9.1 Fitting a Quadratic Model 27
1.9.2 Calculating Second Differences 28
1.10 Logistic Functions and Models 29
1.10.1 Fitting a Logistic Model 29
1.11 Cubic Functions and Models 30
1.11.1 Fitting a Cubic Model 30
1.12 Cyclic Functions and Models 31
1.12.1 Graphing a Sine Function 31
1.12.2 Fitting a Sine Model 31
Chapter 2 Describing Change: Rates 33
2.1 Measures of Change over an Interval 33
2.1.1 Calculating Change 33
2.1.2 Calculating Average Change 33
2.1.3 Calculating Percentage Change 34
2.1.4 Graphing a Secant Line 34
2.4 Rates of Change – Numerical Limits and Nonexistence 35
2.4.2 Numerically Estimating Rate of Change 35
2.4.4 Graphing the Tangent Line 36
Chapter 3 Determining Change: Derivatives 37
3.1 Simple Rate-of-Change Formulas 37
3.1.1 Writing the derivative of a regression function 37
3.1.1a Accessing coefficients from a regression function 37
3.1.1b Calculating with coefficients from the regression function 38
3.1.1c Using coefficients from the regression function in Y= 38
3.1.2 Evaluating a function in Y= using coefficients from a regression 38
3.4 Rates of Change for Composite Functions 39
3.4.1 Calculations involving the Chain Rule 39
3.4.1a Using Y= with the Chain Rule 39
3.4.1b Graphing a function involving the Chain Rule 39
Chapter 4 Analyzing Change: Applications of Derivatives 40
4.0 nDeriv — TI’s Numerical Derivative Routine 40
4.0.1 Using nDeriv to Calculate and Graph 40
4.0.1a Calculating with nDeriv 40
4.0.1b Graphing with nDeriv 41
4.0.1c Calculating with nDeriv in Y= 41
4.1 Linearization and Estimates 42
4.1.1 Graphing and Calculating with Linearizations 42
4.1.1a Graphing a linearization 42
4.1.1b Calculating with a linearization 42
4.2 Relative Extreme Points 43
4.2.1 Solving for Zeros of the Derivative 43
4.4 Inflection Points and Second Derivatives 44
4.4.1 Locating an Inflection Point 44
Chapter 5 Accumulating Change: Limits of Sums and the Definite Integral 45
5.2 Limits of Sums and the Definite Integral 45
5.2.1 Using NUMINTL to Estimate the Accumulated Change 45
5.2.1a NUMINTL with Right-Rectangles 45
5.2.1b NUMINTL with Left-Rectangles 46
5.2.1c NUMINTL with Midpoint-Rectangles 47
5.6 The Definite Integral - Algebraically 48
5.6.1 fnInt — TI’s numerical integration routine 48
5.6.2 Evaluating a Piecewise-Defined Integral 49
5.7 Differences of Accumulated Change 50
5.7.1 Calculating Area of Between Two Intersecting Curves 50
Chapter 6 Analyzing Accumulated Change: Integrals in Action 51
6.1 Perpetual Accumulation and Improper Integrals 51
6.1.1 Numerically Evaluating an Improper Integral 51
6.3 Calculus in Economics: Demand and Elasticity 52
6.3.1 Locating the Point of Unit Elasticity 52
Chapter 7 Ingredients of Multivariable Change: Models, Graphs, Rates 53
7.1 Multivariable Functions and Contour Graphs 53
7.1.0 Evaluating a Multivariable Function 53
7.1.3 Solving a Multivariable Function for One Input Variable 53
7.2 Cross-Sectional Models and Rates of Change 55
7.2.1 Fitting a Cross-Sectional Equation 55
7.3 Partial Rates of Change 56
7.3.1 Evaluating a Partial Derivative at a Point 56
7.4 Compensating for Change 57
7.4.1 Evaluating the Derivative at a Point 57
7.4.2 Evaluating the Slope of a Tangent Line at a Point 57
Chapter 8 Analyzing Multivariable Change: Optimization 58
8.2 Multivariable Optimization 58
8.2.1 Solving a system of two linear equations 58
8.3 Optimization under Constraints 59
8.3.1 Solving a system of three linear equations 59
8.3.2 Identifying the type of constrained point 60
Preliminaries

0.1 Setup and Calculations

0.1.0 Turning the Calculator ON or OFF

• Use ON at the bottom left of the key pad
to turn the calculator on. If the calculator
is not on the home screen when turned on,
2ND MODE [QUIT] returns to the home
screen.
• To turn the calculator OFF, use 2ND ON.
The 2ND function key is the blue key near
the top left of the key pad.

0.1.1 Settings

This guide assumes that the calculator has been setup as follows:

0.1.1a Mode
• settings should be as in the screenshot.
Use the cursor and ENTER keys to
change any settings that are incorrect. The
cursor keys, , are located near the
top right of the keypad.
• QUIT (2ND MODE) to exit the MODE screen.

0.1.1b Statistical Setup
• Specify the statistical setup using
STAT

• 5 selects 5: SetUpEditor

• Type 2ND 1 , 2ND 2 , 2ND 3 , 2ND 4 ,
2ND 5 , 2ND 6
Commas are necessary. The comma key is
located directly above 7 on the keypad.
• ENTER executes the setup command and
returns “Done” when the calculator has
completed the task.

©2012 Cengage Learning. All rights reserved. May not be scanned, copied or duplicated,
or posted to a publicly accessible website, in whole or in part.
2
5e Calculus Concepts; LaTorre, et al.
TI-84 Calculator Guide
• STAT ENTER shows the complete set

of lists.
• QUIT (2ND MODE) exits the list editor
and returns to the home screen.

0.1.1c Graphing Window Format
• Specify the graphing window setup using
FORMAT (2ND ZOOM).
The ZOOM key is located directly under
the screen.
ENTER
• UQsUeI tTh e( 2cNurDso Mr aOnDd E) exits tkheey sg rtaop chhinagn ge
waniny dsoewtt ifnogrsm tahta stc arreee nin acnodr rreectut.r n s to the
home screen.

0.1.2 Calculating

When evaluating expressions using a calculator, the order of operations is important.
*It may be necessary to use parentheses that do not appear in handwritten expressions.
* Negative signs are not the same as minus signs on a TI calculator.
The negative sign (–) key is along the bottom row of the keypad.
The minus key is third from the bottom in the right column of the keypad.

Practice Expressions:

−7−3
•
−2(−5)
−4−15−2
•

1−4

−108 768
• −
9 −24

(2+4)2
•
(5−3)2

©2012 Cengage Learning. All rights reserved. May not be scanned, copied or duplicated,
or posted to a publicly accessible website, in whole or in part.
3
Preliminaries
TI-84 Calculator Guide
102 −52
•
82 +32 −(−2)
21(−106)−35(−40)
•

2(51−58)

0.1.3 Accessing 2ND and ALPHA Functions

Most of the keys on the TI-84 have multiple uses. A key’s main function is indicated on the
key itself. Above the key are indicated the two other functions in blue and green type.

• Blue type indicates a function accessed using the blue 2ND key near the top left of the
keypad before typing the desired key

For example, to access the symbol for
use in calculations type 2ND ex .

• Green type indicates a function accessed using the green ALPHA key directly
beneath the 2ND key.
For example, to access the letter V, type
ALPHA 6.

©2012 Cengage Learning. All rights reserved. May not be scanned, copied or duplicated,
or posted to a publicly accessible website, in whole or in part.
4
5e Calculus Concepts; LaTorre, et al.
TI-84 Calculator Guide
0.1.4 Using ENTRY and ANS to Reuse Expressions

The TI-84 can recall previous expressions it has evaluated. The TI-84 stores the last 25
expressions that were evaluated on the home screen, even after the screen has been
cleared.

• To recall a previously evaluated expression, use ENTRY (2ND ENTER).
Repeatedly typing ENTRY recalls expressions from most recent entered to earliest
entered.
• After recalling an expression to the home screen, the cursor keys as well as delete,
DEL, and insert, INS (2ND DEL) can be used to modify the expression.
• ENTER is used to re-evaluate the expression.

0.1.5 Storing and Recalling Values

The TI-84 can store a numerical value for later use in an expression or calculation. Each
of the alpha keys can be used to access a storage location.

• The STO key stores a number for later use. With a number or expression on the
home screen, type STO A (ALPHA MATH) to store the number into storage
location A. Any of the letters can be used for storage. It is best to avoid X because
the calculator uses this position to store calculated input values.

3
For example, to store the real number equivalent of (to 32 decimal-place
2+5
accuracy) in T...
3
• Type the expression on
2+5
the home screen
• Type STO T (ALPHA 4)
• ENTER evaluates the
expression and stores the result
in T.

• The recall the number stored in an alpha location, type the letter (either alone or in an
expression).

For example, to use the number that has been stored in T while evaluating another
expression...
• Type the expression 24−5T
(Use ALPHA 4 to type T.)
• ENTER evaluates the expression.

©2012 Cengage Learning. All rights reserved. May not be scanned, copied or duplicated,
or posted to a publicly accessible website, in whole or in part.
Chapter 1 Ingredients of Change: Functions and Limits

1.1 Functions—Four Representations

1.1.1-1.1.2 Entering and evaluating a function (CC5e p. 4)
Given g(t)=3et −2t, evaluate g(4).

1.1.1 To enter a function into Y1 in the equation editor...
• Y= (located directly under the calculator
screen) opens the equation editor

• Enter the right side of the equation into Y1
using 2ND LN [e^] for e and X,T,θ,n for x

 X,T,θ,n is used to represent the input variable in a function. The other letters
(obtained using ALPHA ) are storage units that hold a specific number.

• 2ND MODE [QUIT] returns to the home
screen

1.1.2 To evaluate the output value of the function entered in Y1...
• VARS accesses the Variables
screen

• Highlight Y-VARS using  (right
arrow) selects the
VARS Y-VARS menu

• 1 (or ENTER) selects 1: Function

• 1 (or ENTER) selects 1: Y1

( keystroke summary)
 VARS Y-VARS Function Y1

• ( 4 ) indicates the input value to be
evaluated

• ENTER evaluates g at t = 4

 The output is g(4) ≈155.794

©2012 Cengage Learning. All rights reserved. May not be scanned, copied or duplicated,
or posted to a publicly accessible website, in whole or in part.
6 5e Calculus Concepts; LaTorre, et al.
TI-84 Calculator Guide

1.1.2a To set the number of decimal places report by the calculator...
• MODE accesses the mode screen

Mode should usually be set as in
the near right screenshot.

• To set rounding to three decimal places, highlight 3 on the decimal options line...
 (down arrow) to the line
beginning with FLOAT then
    (left arrow, four times)

• 2ND MODE [QUIT] returns to
the home screen

1.1.2b To re-evaluate a previous entry...
• 2ND ENTER [ENTRY] copies a
previous command (that has not yet
been deleted)

• ENTER re-evaluates the function

1.1.2c To edit a previous entry...
• 2ND ENTER [ENTRY] copies
the previous command

• Use  to move the cursor over the
4 then change 4 to 9

• ENTER re-evaluates the function

 The output isg(9)≈24,291.252

1.1.3 Using Equation Solver (CC5e p.6)
Forg(t)=3et −2t, solve g(t)=300.

• MATH 0 (0: Solver) accesses a
solver dialog screen similar to the
near right screenshot

• Select the top line using  (up
arrow) to access the EQUATION
SOLVER screen

©2012 Cengage Learning. All rights reserved. May not be scanned, copied or duplicated,
or posted to a publicly accessible website, in whole or in part.
Chapter 1 7
TI-84 Calculator Guide

• Complete the equation to be solved
so that it reads 0 = Y1 – 30 then
ENTER (or ) to return to the
solver dialog screen

• Position the cursor on the X = line
(shown as X = 0 in the far right
screenshot)

• ALPHA ENTER [SOLVE]
returns a solution to the equation

 When g(t)=300, t ≈4.636

For an equation with only one solution, any value in the domain of the function will
return the solution. For an equation with multiple solutions, the solution closer to the
starting value is returned.

1.1.4 Graphing a function (CC5e p. 5, Example 1)
Graph p(t)=80(1.013t)million people where t is the number of years since the end of 1900,
0≤t ≤100.

• Enter the function into Y1...
• Y = opens the equation editor

• With the cursor located to the
right of the = on the Y1= line,
CLEAR any content from Y1

• Enter the formula for p(t) into
4Y1

To set the graph’s input interval...
• WINDOW (located directly under
the calculator screen)
• Set Xmin to –10 by typing (-) 10
• Set Xmax to 10 by typing 10

©2012 Cengage Learning. All rights reserved. May not be scanned, copied or duplicated,
or posted to a publicly accessible website, in whole or in part.