There are two ways to define the derivative of a function f at a given number a:(see attached photo)Choose the ANSWERS that correctly and strongly justify why we take h → 0 in equation (B).We always have a = 0, so the two equations agree with h = b.h is the run (denominator) of the slope for the secant line that passes through (a, f(a)) and (a + h, f(a + h)), and we want this run to approach zero to get the slope of the tangent line.h is equal to zero.Comparing equations (A) and (B), we see that so taking h → 0 is equivalent to b → a.Since f'(a) is the limit of a difference quotient (ratio of the difference in outputs to the difference in inputs), h = final input value - initial value number a:(A)(B)f'(a)(a) = limb→af' (a) = limh→0f(b) – f(a)b-af(a+h) —h

Answered: Image /qna-images/answer/2428f307-ad00-4d3c-a8c3-3cfa5636a3c2.jpg

Answered: number a: (A) (B) f'(a) (a) = lim b→a…

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

There are two ways to define the derivative of a function f at a given number a:

(see attached photo)

Choose the ANSWERS that correctly and strongly justify why we take h → 0 in equation (B).

- We always have a = 0, so the two equations agree with h = b.
- h is the run (denominator) of the slope for the secant line that passes through (a, f(a)) and (a + h, f(a + h)), and we want this run to approach zero to get the slope of the tangent line.
- h is equal to zero.
- Comparing equations (A) and (B), we see that so taking h → 0 is equivalent to b → a.
- Since f'(a) is the limit of a difference quotient (ratio of the difference in outputs to the difference in inputs), h = final input value - initial value