Problem 2. For every real number a # 0, for every nonnegative integer n, for the function f(x) = x^, simplify the limit, f(q. a) f(a) (q. a) — a - Evaluate your simplified limit using the formula for a finite geometric sum, q" - 1 9-1 lim q→1 1+q+q² + +qn-1: ... Use this to compute f'(a) for a 0. =

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Problem 1. For every real number a, compute the derivative of y = x4 at
x = a as a limit of a difference quotient. Show your work.
Problem 2. For every real number a # 0, for every nonnegative integer n,
for the function f(x) x^, simplify the limit,
I
lim
q→1
f(q. a) – f(a)
-
(q. a) — a
-
Evaluate your simplified limit using the formula for a finite geometric sum,
q" - 1
9-1
1+q+q² + ··· + q-1
...
Use this to compute f'(a) for a 0.
=
Transcribed Image Text:Problem 1. For every real number a, compute the derivative of y = x4 at x = a as a limit of a difference quotient. Show your work. Problem 2. For every real number a # 0, for every nonnegative integer n, for the function f(x) x^, simplify the limit, I lim q→1 f(q. a) – f(a) - (q. a) — a - Evaluate your simplified limit using the formula for a finite geometric sum, q" - 1 9-1 1+q+q² + ··· + q-1 ... Use this to compute f'(a) for a 0. =
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