(4) Q4 MULTIPLE CHOICE One answer only. If f,g: RR are functions such that f and fg are differentiable, then g is differentiable. a. False, here is a counter-example: f(x) = x, g(x) = sin(1/x). b. True, by algebraic differentiation theorem because g = (fg)/f is the quotient of two differentiable functions. c. True, by the algebraic differentiation theorem: if g is not differentiable, then fg is not differentiable either. d. False, here is a counter-example: f(x) = x², g(x) = √√|x|.
(4) Q4 MULTIPLE CHOICE One answer only. If f,g: RR are functions such that f and fg are differentiable, then g is differentiable. a. False, here is a counter-example: f(x) = x, g(x) = sin(1/x). b. True, by algebraic differentiation theorem because g = (fg)/f is the quotient of two differentiable functions. c. True, by the algebraic differentiation theorem: if g is not differentiable, then fg is not differentiable either. d. False, here is a counter-example: f(x) = x², g(x) = √√|x|.
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) Q4 MULTIPLE CHOICE One answer only
If f, g: R → R are functions such that ƒ and fg are differentiable, then g is differentiable.
a. False, here is a counter-example: f(x) = x, g(x) = sin(1/x).
=
b. True, by algebraic differentiation theorem because g
functions.
(fg)/f is the quotient of two differentiable
c. True, by the algebraic differentiation theorem: if g is not differentiable, then fg is not differentiable
either.
d. False, here is a counter-example: f(x) = x², g(x) = √√√x|.
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