Consider this function y = f(x) on the domain (-, ). f(x) = x sin( 8 x )+ 20 if
ID: 2855888 • Letter: C
Question
Consider this function y = f(x) on the domain (-, ). f(x) = x sin( 8 x )+ 20 if x 0 20 if x = 0 (a) If x 0 , f '(x)= sin( 8 x) 8 x·cos( 8 x) Correct: Your answer is correct. (b) Answer these multiple choice questions: (1) lim_(x->0) f(x) = Does not exist 20 8 0 - Correct: Your answer is correct. (2) lim_(h->0) f(h)f(0) h = Does not exist 20 8 0 - (3) f '(0)= Does not exist 20 8 0 - Incorrect: Your answer is incorrect. (4) f(x) is continuous for all x True False (5) f(x) is differentiable for all x True False
Explanation / Answer
Derivative of f(x) is sin(8x)+8cos(8x) , which is continues over domain.
Hence given function is differentiable and continoues over domain.