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Let g be a function, defined in terms of some other

Let g be a function, defined in terms of some other

Advanced Engineering Mathematics
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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Please do part b,c,d,e.

201617: functions, integrals. Let g be a function, defined in terms of some other function f, such that g(x) = f(x) f(x) + f(1 − x). Suppose that f is non-zero on the interval (0, 1) and has known derivative f'. a. Show that g(1 − x) = 1 – g(x). What is g(¹)? 2 b. Hence, by considering 13 0 c. Calculate g' in terms of f and f'. What is g'()? d. Suppose that f'(0) = 0 = f(0), and f(1) ‡ 0. Calculate g'(0) and g'(1). e. Suppose that f(x) = 0 for x ≤ 0. and x ≥ 1. Describe the behaviour of g(x) for x ≤ 0 f. Sketch g(x), given that f(x) = g(x) dx, calculate 0, x², So g(x) dx. for x ≤ 0; for x > 0.
Transcribed Image Text:201617: functions, integrals. Let g be a function, defined in terms of some other function f, such that g(x) = f(x) f(x) + f(1 − x). Suppose that f is non-zero on the interval (0, 1) and has known derivative f'. a. Show that g(1 − x) = 1 – g(x). What is g(¹)? 2 b. Hence, by considering 13 0 c. Calculate g' in terms of f and f'. What is g'()? d. Suppose that f'(0) = 0 = f(0), and f(1) ‡ 0. Calculate g'(0) and g'(1). e. Suppose that f(x) = 0 for x ≤ 0. and x ≥ 1. Describe the behaviour of g(x) for x ≤ 0 f. Sketch g(x), given that f(x) = g(x) dx, calculate 0, x², So g(x) dx. for x ≤ 0; for x > 0.
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