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Let 2³/2 sin (0) 0; (x = 0) f(x) = :{" i Calculate f'(0) using the definition. Hint see notes/video on the derivative of a sin 1/x. ii Calculate f'(x) for x 0. Hint: Use the product rule and the chain rule. iii Is f'(x) continuous at x = 0? Hint: See notes/video on the derivative of a sin 1/x

Let 2³/2 sin (0) 0; (x = 0) f(x) = :{" i Calculate f'(0) using the definition. Hint see notes/video on the derivative of a sin 1/x. ii Calculate f'(x) for x 0. Hint: Use the product rule and the chain rule. iii Is f'(x) continuous at x = 0? Hint: See notes/video on the derivative of a sin 1/x

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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4. Let f(x) = { x/² sin ; (x+ 0) 0; (x = 0) i Calculate f'(0) using the definition. Hint see notes/video on the derivative of x sin 1/x. ii Calculate f'(x) for r # 0. Hint: Use the product rule and the chain rule. iii Is f'(x) continuous at x = 0? Hint: See notes/video on the derivative of x sin 1/x
Transcribed Image Text:4. Let f(x) = { x/² sin ; (x+ 0) 0; (x = 0) i Calculate f'(0) using the definition. Hint see notes/video on the derivative of x sin 1/x. ii Calculate f'(x) for r # 0. Hint: Use the product rule and the chain rule. iii Is f'(x) continuous at x = 0? Hint: See notes/video on the derivative of x sin 1/x
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