Mathematics

Mathematics

Problem

Consider the function f(x)={x2,x≤1,2x−1,x>1.f(x)=\begin{cases} x^{2}, & x\le 1,\\ 2x-1, & x>1. \end{cases} Answer the following: a. (i) Verify the continuity of ff at x=1x=1. b. (ii) Determine whether ff is differentiable at x=1x=1 by evaluating the appropriate limits. State your conclusion clearly.

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