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Verify the given linear approximation at $ a = 0. $ Then determine the values of $ x $ for which the linear approximation is accurate to within 0.1.$ \sqrt [4]{1 + 2x} \approx 1 + \frac {1}{2}x $

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Calculus 1 / AB

Chapter 3

Differentiation Rules

Section 10

Linear Approximation and Differentials

Derivatives

Differentiation

Oregon State University

Harvey Mudd College

Baylor University

Lectures

04:40

In mathematics, a derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a moving object with respect to time is the object's velocity. The concept of a derivative developed as a way to measure the steepness of a curve; the concept was ultimately generalized and now "derivative" is often used to refer to the relationship between two variables, independent and dependent, and to various related notions, such as the differential.

44:57

In mathematics, a differentiation rule is a rule for computing the derivative of a function in one variable. Many differentiation rules can be expressed as a product rule.

02:21

Verify the given linear ap…

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04:55

Find the linear approximat…

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okay. We know the four through of one plus two acts. Amino X zero gives us one there for the derivative would be 1/2 times one plus. If you plug in zero, we end up with 1/2. Therefore, we have the four through of one plus two. Axe equals one plus 1/2 axe. Therefore verifying this We know we have 0.1 is less than the four through of done pushed you axe on a swan. And this 1/2 acts, which is less than 0.1. Therefore we have 0.9 is less than four through of one plus two acts minus 1/2 axe. Just lost them 1.1. So we have. Why's your 0.9? White is 1.1 to the values would be between the of 0.3689 and 0.6777

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