Maurice Tutor

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Teaching Since: May 2017
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  • MCS,PHD
    Argosy University/ Phoniex University/
    Nov-2005 - Oct-2011

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  • Professor
    Phoniex University
    Oct-2001 - Nov-2016

Category > Management Posted 04 Feb 2018 My Price 7.00

sequence of quotients

Define f : R → R by f (x) = x sin (1/x) if x ≠ 0 and f (0) = 0. Determine whether or not f is differentiable at x = 0. We see from Example 1.4(a) that it is possible for a function to be continuous at a point without being differentiable at the point. On the other hand, it is easy to prove that if f is differentiable at a point, then it must also be continuous there.

 

Example 1.4

(a) Let f (x) = |x| for each x ∈ R, and let xn = (–1)n/n for n ∈ N. Then the sequence (xn) converges to 0, but the corresponding sequence of quotients does not converge. (See Figure 2.)

Answers

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Status NEW Posted 04 Feb 2018 07:02 PM My Price 7.00

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