= 4. Consider the function f [0, 1] → R defined so that f(0) x = (1/(n+1), 1/n], where n is any positive integer, f(x) = 1/n. 0, and, for all (a) Draw the graph of the function f. (b) Is f differentiable at 0? If so, what is f'(0)? Prove your assertion. (c) What properties does the function f have? (Bounded? Differentiable? Con- tinuous? Surjective? Injective? Monotonic?)

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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=
4. Consider the function f [0, 1] → R defined so that f(0)
x = (1/(n+1), 1/n], where n is any positive integer, f(x) = 1/n.
0, and, for all
(a) Draw the graph of the function f.
(b) Is f differentiable at 0? If so, what is f'(0)? Prove your assertion.
(c) What properties does the function f have? (Bounded? Differentiable? Con-
tinuous? Surjective? Injective? Monotonic?)
Transcribed Image Text:= 4. Consider the function f [0, 1] → R defined so that f(0) x = (1/(n+1), 1/n], where n is any positive integer, f(x) = 1/n. 0, and, for all (a) Draw the graph of the function f. (b) Is f differentiable at 0? If so, what is f'(0)? Prove your assertion. (c) What properties does the function f have? (Bounded? Differentiable? Con- tinuous? Surjective? Injective? Monotonic?)
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