EBK PRECALCULUS W/LIMITS
EBK PRECALCULUS W/LIMITS
4th Edition
ISBN: 9781337516853
Author: Larson
Publisher: CENGAGE CO
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Concept explainers

Limits
When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topic…
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Chapter 2, Problem 21RE

(a)

To determine

Use the Intermediate Value Theorem and the table feature of a graphing utility to find intervals one unit in length in which the polynomial function is guaranteed to have a zero.

(a)

Expert Solution
Check Mark

Answer to Problem 21RE

The answer is −1,0

Explanation of Solution

Given:

  f(x)=3x3−x2+3

The intermediate value theorem is "If f is continuous on a closed interval [a,b], , and c is any number between f(a) and f(b) inclusive, then there is at least one number x in the closed interval such that f(x)=c= . The equation given to us are continuous.

So for the function f(x)=3x3−x2+3 if substitute 0 get 3 as a resultant and if substitute-1 get −1 as a resultant. So the values at both these points changed it it's sign.

Therefore in this interval there must be a zero.

So the answer is −1,0

(b)

To determine

Adjust the table to approximate the zeros of the function to the nearest thousandth Use the zero or root feature of the graphing utility to verify your results.

(b)

Expert Solution
Check Mark

Answer to Problem 21RE

Graph is shown below.

Explanation of Solution

Given:

  f(x)=3x3−x2+3

Use the graphing utility find the values at which these zeros occur. So the value obtained by using computer acid is −0.900. Use the graphing utility to draw the graph and see that there is a zero in this region. So the graph is,

  EBK PRECALCULUS W/LIMITS, Chapter 2, Problem 21RE

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Chapter 2, Problem 22RE

Chapter 2 Solutions

EBK PRECALCULUS W/LIMITS

Ch. 2.1 - Prob. 1ECh. 2.1 - Prob. 2ECh. 2.1 - Prob. 3ECh. 2.1 - Prob. 4ECh. 2.1 - Prob. 5ECh. 2.1 - Prob. 6ECh. 2.1 - Prob. 7ECh. 2.1 - Prob. 8ECh. 2.1 - Prob. 9ECh. 2.1 - Prob. 10E
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Limits and Continuity; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=9brk313DjV8;License: Standard YouTube License, CC-BY