CALCULUS:EARLY TRANS.(LL)-W/ACCESS
CALCULUS:EARLY TRANS.(LL)-W/ACCESS
4th Edition
ISBN: 9781319308858
Author: Rogawski
Publisher: MAC HIGHER
Question
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Chapter 4, Problem 1CRE
To determine

Estimate using the Linear Approximation or linearization. Also, use a calculator to estimate the error.

Expert Solution & Answer
Check Mark

Answer to Problem 1CRE

Solution:

The error is 3.448×105.

Explanation of Solution

Given:

The expression is 8.1132.

Formula used:

Linear Approximation:

Δf=f(a)Δx

Calculation:

The expression is 8.1132.

Let f(x)=x13, a=8andΔx=0.1.

Now, find the derivative of the function f(x) with respect to x.

f(x)=13x23

Find the value of f(a).

f(a)=13a23=13(8)23=13(23)23=13(14)=112

Now, find the estimate using Linear Approximation.

Use the formula: Δf=f(a)Δx

Δf=f(a)Δx=112(0.1)=0.00833333333

Use the calculator to find the value of 8.1132.

We can rewrite it as:

(8.1)0.333332

CALCULUS:EARLY TRANS.(LL)-W/ACCESS, Chapter 4, Problem 1CRE

(8.1)0.333332=2.008298852=0.00829885

Now, find the error in the Linear Approximation.

Error=|0.008298850.00833333333|=0.00003448=3.448×105

Hence, the error is 3.448×105.

Conclusion:

With the help of the formula, wecould figure out the error in the Linear Approximation.

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Chapter 4 Solutions

CALCULUS:EARLY TRANS.(LL)-W/ACCESS

Ch. 4.1 - Prob. 7ECh. 4.1 - Prob. 8ECh. 4.1 - Prob. 9ECh. 4.1 - Prob. 10ECh. 4.1 - Prob. 11ECh. 4.1 - Prob. 12ECh. 4.1 - Prob. 13ECh. 4.1 - Prob. 14ECh. 4.1 - Prob. 15ECh. 4.1 - Prob. 16ECh. 4.1 - Prob. 17ECh. 4.1 - Prob. 18ECh. 4.1 - Prob. 19ECh. 4.1 - Prob. 20ECh. 4.1 - Prob. 21ECh. 4.1 - Prob. 22ECh. 4.1 - Prob. 23ECh. 4.1 - Prob. 24ECh. 4.1 - Prob. 25ECh. 4.1 - Prob. 26ECh. 4.1 - Prob. 27ECh. 4.1 - Prob. 28ECh. 4.1 - Prob. 29ECh. 4.1 - Prob. 30ECh. 4.1 - Prob. 31ECh. 4.1 - Prob. 32ECh. 4.1 - Prob. 33ECh. 4.1 - Prob. 34ECh. 4.1 - Prob. 35ECh. 4.1 - Prob. 36ECh. 4.1 - Prob. 37ECh. 4.1 - Prob. 38ECh. 4.1 - Prob. 39ECh. 4.1 - Prob. 40ECh. 4.1 - Prob. 41ECh. 4.1 - Prob. 42ECh. 4.1 - Prob. 43ECh. 4.1 - Prob. 44ECh. 4.1 - Prob. 45ECh. 4.1 - Prob. 46ECh. 4.1 - Prob. 47ECh. 4.1 - Prob. 48ECh. 4.1 - Prob. 49ECh. 4.1 - Prob. 50ECh. 4.1 - Prob. 51ECh. 4.1 - Prob. 52ECh. 4.1 - Prob. 53ECh. 4.1 - Prob. 54ECh. 4.1 - Prob. 55ECh. 4.1 - Prob. 56ECh. 4.1 - Prob. 57ECh. 4.1 - Prob. 58ECh. 4.1 - Prob. 59ECh. 4.1 - 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Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:PEARSON
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Calculus: Early Transcendentals
Calculus
ISBN:9781319050740
Author:Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:W. H. Freeman
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Precalculus
Calculus
ISBN:9780135189405
Author:Michael Sullivan
Publisher:PEARSON
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Calculus: Early Transcendental Functions
Calculus
ISBN:9781337552516
Author:Ron Larson, Bruce H. Edwards
Publisher:Cengage Learning