Problem

Verify the given linear approximation at $a=0 .$ …

02:21

Problem 6 Easy Difficulty

Find the linear approximation of the function
$g(x)=\sqrt[3]{1+x}$ at $a=0$ and use it to approximate the
numbers $\sqrt[3]{0.95}$ and $\sqrt[3]{1.1}$ . Illustrate by graphing $g$ and
the tangent line.

Answer

$L(x)=1+\frac{1}{3} x, \quad \sqrt[3]{0.95} \approx 0.9833, \quad \sqrt[3]{1.1} \approx 1.033$

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Calculus 1 / AB

Essential Calculus Early Transcendentals

Chapter 2

DERIVATIVES

Section 8

Linear Approximations and Differentials

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Video Transcript

Okay, So for this program, we start away that a function Joe fix. So first we need to compute its curative, since we want to fight the memorization that you prime mix, which is 1/3 1 Prospects to the, um minus 2/3 set of Familiarization is given by she off. Hey, plus G prime off eight times X minus A. So, in this case, a course zero. So we immediately have one plus 1/3 picks. So this is the remilitarization and the we can usually visit glamorization to approximate the following values. So first is, um, 0.95 to the cubic roots. Um, in fact, this is the value off G off miners, their 0.5 So by arleen Ooh, approximation we have We can use ello off miners syrup going 05 to approximate this value, which is, um, 0.983 30 meets the wrong this and for the other one, we just simply we do the same thing because this equals two g off their 20.1. And we're just project and put 0.1 into ella. So we have this result 1.33 toe. Approximate Miss given value

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