This question has two distinct parts: a) Let g: R→ R be a differentiable function at x = a. Show that xg(a)- ag(x) x - a lim x-a = g(a) - ag'(a)
This question has two distinct parts: a) Let g: R→ R be a differentiable function at x = a. Show that xg(a)- ag(x) x - a lim x-a = g(a) - ag'(a)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:4. This question has two distinct parts:
a) Let g: R→ R be a differentiable function at x = a. Show that
xg(a)- ag(x)
lim
x-a
x-a
= g(a) - ag'(a)
b) Let f: R→ R be a differentiable function at x = 0, and
f(x + y) = f(x)f(y),
Show that f is differentiable at every point x.
for every x, y ER
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