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Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
Publisher: Cengage Learning
ISBN: 9781337552516

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Section
BuyFindarrow_forward

Calculus: Early Transcendental Fun...

7th Edition
Ron Larson + 1 other
Publisher: Cengage Learning
ISBN: 9781337552516
Chapter 2, Problem 35RE
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 9 x 3 + 729 x + 9

To determine

To graph: The function to estimate the limit limx9x3+729x+9. Use a table to reinforce the conclusion and then find the limit by analytic methods.

Explanation of Solution

Given:

f(x)=x3+729x+9

Formula Used:

limxcx=c————— (1)

limxcf(x)=limxcg(x)=g(c)————— (2)

Graph:

Use Ti83 calculator to graph the function and its limit. The following steps are need.

Step1. Press ON button.

Step2. Press Y= button and write the function Y1=x3+729x+9.

Step3. Press 2nd button.

Step4. Press GRAPH button.

Step5. Enter some values of X that approaches to 9.

Step6. Press ZOOM and chose number 6.

Step7. Press ENTER button.

Step8. Input X=9

Step9. Press ENTER button.

And the graph is shown below and value of limit is 243.

To obtain the limit of the given function, we draw a straight passing through the point x=9. It can be observed that the line x=9 crosses the function at y=243

We then use tabular method to estimate the limit

x -9.01 -9.001 -9 -8.999 -8.99
f(x) 243.7201 243.027001 ? 242.973001 242

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Chapter 2 Solutions

Calculus: Early Transcendental Functions
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Continuity of a Composite Function In Exercises...Ch. 2.4 - Continuity of a Composite Function In Exercises...Ch. 2.4 - Continuity of a Composite Function In Exercises...Ch. 2.4 - Finding Discontinuities Using Technology In...Ch. 2.4 - Finding Discontinuities Using Technology In...Ch. 2.4 - Finding Discontinuities Using Technology In...Ch. 2.4 - Finding Discontinuities Using Technology In...Ch. 2.4 - Testing for Continuity In Exercises 75-82,...Ch. 2.4 - Testing for Continuity In Exercises 75-82,...Ch. 2.4 - Testing for Continuity In Exercises 75-82,...Ch. 2.4 - Testing for Continuity In Exercises 75-82,...Ch. 2.4 - Testing for Continuity In Exercises 75-82,...Ch. 2.4 - Testing for Continuity In Exercises 75-82,...Ch. 2.4 - Testing for Continuity In Exercises 75-82,...Ch. 2.4 - Testing for Continuity In Exercises 75-82,...Ch. 2.4 - Existence of a Zero In Exercises 83-88, explain...Ch. 2.4 - Existence of a Zero In Exercises 83-88, explain...Ch. 2.4 - Existence of a Zero In Exercises 83-88, explain...Ch. 2.4 - 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