can the fact in solution of question number 10 use to solve this question? any expert please help if you know how to use it Consider the functionif a € Qf(r) =if æ ¢ Q.Prove that f'(0) = 0.Hint: The fact stated in Question 10 of Problem Set 2 is useful. 10) First, we prove the forward direction. Assume lim f(r) = 0. We need to show thatエ→alim |f(r)| = 0. Fix e > 0. We need to find some 8 > 0 such that whenever 0 < |r - a| < 8,we have ||f(r)| - 0| < e. Since lim f(x) = 0, we can choose d > 0 such that whenever0< |x – a| < 8, we have |f(x) – 0| < e. With this d, it follows that whenever 0 < |r – a| < 8,we have ||f(x)| – 0| = |f(x)| < e as required.Conversely, assume lim |f(x)| = 0. We need to show that lim f(x) = 0. Fix e > 0. Weエ→aエ→4need to find some o > 0 such that whenever 0 < |a - al < 8, we have |f(r) – 0| < e. Sincelim |f(x)| = 0, we can choose ô > 0 such that whenever () < |r-a| < 8, we have || f(x)|- 0| < e.With this d, it follows that whenever 0 < |r – a| < 8, we have |f (x) – 0 = ||f(x)|| < e asrequired.

Name: can the fact in solution of question number 10 use to solve this quest
Uploaded: 2024-03-20T07:06:27.000Z
Channel: Bartleby
Description: can the fact in solution of question number 10 use to solve this question? any expert please help if you know how to use it Consider the functionif a € Qf(r) =if æ ¢ Q.Prove that f'(0) = 0.Hint: The fact stated in Question 10 of Problem Set 2 is usef