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2. Suppose that f is defined on (0, b) and that f is differentiable at c € (0, b). (Do not assume that f is differentiable at any other points.) Evaluate each of the following limits; the answers will be in terms of c, f'(c), etc. f(x)-f(c) xf(c)-cf(x) a) lim b) lim x-c c) lim f(x²)-f(c) x-√c

2. Suppose that f is defined on (0, b) and that f is differentiable at c € (0, b). (Do not assume that f is differentiable at any other points.) Evaluate each of the following limits; the answers will be in terms of c, f'(c), etc. f(x)-f(c) xf(c)-cf(x) a) lim b) lim x-c c) lim f(x²)-f(c) x-√c

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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2. Suppose that f is defined on (0, b) and that f is differentiable at ce (0, b). (Do not assume that f is differentiable at any other points.) Evaluate each of the following limits; the answers will be in terms of c, f'(c), etc. f(x) - f(c) xf(c) - cf(x) x²-c² X= a) lim X-C b) lim - c) lim x→ √e f(x²) - f(c) x-√c
Transcribed Image Text:2. Suppose that f is defined on (0, b) and that f is differentiable at ce (0, b). (Do not assume that f is differentiable at any other points.) Evaluate each of the following limits; the answers will be in terms of c, f'(c), etc. f(x) - f(c) xf(c) - cf(x) x²-c² X= a) lim X-C b) lim - c) lim x→ √e f(x²) - f(c) x-√c
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