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. =
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
Problem 1RQ
Related questions
Question
question2
![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.
=](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F05136949-0414-47eb-a73e-74f55563dd77%2Ff5973ae3-9f93-4c19-aedf-1d095ddfb32a%2Faxvv6zc_processed.jpeg&w=3840&q=75)
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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