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Calculus of a Single Variable

11th Edition
Ron Larson + 1 other
Publisher: Cengage Learning
ISBN: 9781337275361

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Section
BuyFindarrow_forward

Calculus of a Single Variable

11th Edition
Ron Larson + 1 other
Publisher: Cengage Learning
ISBN: 9781337275361
Chapter 1, Problem 33RE
Textbook Problem
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Graphical, Numerical, and Analytic Analysis In Exercises 33–36, use a graphing utility to graph the function and estimate the limit. Use a table to reinforce your conclusion. Then find the limit by analytic methods.

lim x 0 2 x + 9 3 x

To determine

To Graph: Using a graph utility to graph the givenfunction and estimate the limit by analytic methods.

Explanation of Solution

Given:

f(x)=2x+93x

Formula Used:

limxcxn=cn—————– (1)

limxcx=c———————- (2)

limxcf(x)=limxcg(x)=g(c)————— (3)

Calculation: Use Ti83 calculator to graph the function and its limit. These steps are needed.

Step1. Press ON button.

Step2. Press Y= button and write the function Y1=2x+93x.

Step3. Press 2nd button.

Step4. Press GRAPH button.

Step5. Enter some values of X that approaches to 0.

Step6. Press ZOOM and chose number 6.

Step7. Press ENTER button.

Step8. Input X=0

Step9. Press ENTER button.

And the graph is shown below and value of limit is 0.312

To accomplish the limit of the given function, drawing a straight line passing through the point x=0. It may be observed that the line x=0 crosses the function at y=0.33.

We then use tabular method to estimate the limit

x -0.01 -0.001 0 0.001 0.01
f(x) 0.3335 0.3333 ? 0.3333 0.331

By examine the values of the table, we can measure that the value of the limit is 0

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Chapter 1 Solutions

Calculus of a Single Variable
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True or False? 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