Question: Question 4 Let Q be defined by Q(x) = I' sin(1/x) ifx/ 0 ifr =0 Find the error in the following argument showing that Q'(0)

Question 4 Let Q be defined by Q(x) = I' sin(1/x) ifx/ 0 ifr =0 Find the error in the following argument showing that Q'(0) =0. Your answer should explain the problem and indicate how to fix it. (The statement is true, but the proof given is wrong.) Proof: According to Definition 3.1.1 it must be shown Q(h) - Q(0) Q(h) ha sin(1/h) 0 = lim = lim = lim = lim h sin(1/h). h+0 h h+0 h h+0 h h+0 Now use Theorem 2.5.1 with g(x) = x, f(x) = xsin(1/x) and h(x) = -I. Note that since -1

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