Problem

Use a linear approximation (or differentials) to …

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Problem 25 Easy Difficulty

Use a linear approximation (or differentials) to estimate the given number.
$ \sqrt [3]{1001} $

Answer

$\sqrt[3]{1001}=f(1001) \approx f(1000)+d y=10+\frac{1}{200}=10.00 \overline{3} \approx 10.003$

Topics

Derivatives

Differentiation

Calculus: Early Transcendentals

Chapter 3

Differentiation Rules

Section 10

Linear Approximation and Differentials

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Video Transcript

we know that half of axes The cube root of ax Therefore, after prime of axe is 1/3. Remember the explain. It comes down to be the new coefficient times axe to the negative two divided by three, which is equivalent to X to the 1/3. Remember, we don't want any negative experiments over three acts. Cooking in 1002 the 1/3 over 3003 times 4000 gives us 10 over 3000 a one over 300. So now we have the cube root of 1001 is approximately 10 plus one over 300 which is equivalent to 300 Juan over 300.

Amrita B.

Topics

Derivatives

Differentiation

Calculus: Early Transcendentals

Chapter 3

Differentiation Rules

Section 10

Linear Approximation and Differentials

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