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Explain, in terms of linear approximations, why the approximation is reasonable.$(1.01)^{6} \approx 1.06$

$L(0.01)=1+6(0.01)=1.06($ accurate $)$

Calculus 1 / AB

Chapter 3

Derivatives

Section 8

Linear Approximations and Taylor Polynomials

Campbell University

Harvey Mudd College

Baylor University

Boston College

Lectures

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Explain, in terms of linea…

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Linear approximation a. Fi…

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$7-10$ Verify the given li…

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Verify the given linear ap…

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Linear approximationa.…

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in this coming war after shorter. Why given approximation is reasonable. Well, let's assume that you have a function, uh, which is excellent, Powered six, and we'll sign their work of destruction. That would be six Exit E uh, five. Now, let's select this approximation around. So effort, one would be one. And oh, um, prime of one would be since so that we can record the music should function as oh one plus that primal horn times at once one. And that would be one plus six times. Explain this one. Now let's say that we're given X is equal to 1.0 work, and we're trying to approximate this using the Stephen function. So we're gonna put 1.18 x here. So we finally musician as what? Waas six times 1101 form and which gives us one on your six. So they've given approximation of Oh, when's your want to the six. He's about one point, um, 06 issue need reasonable

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