2 votes 2 votes Consider the function $f(x)=\begin{cases} \int_0^x \{5+ \mid 1-y \mid \} dy & \quad if \: x>2 \\ 5x+2 & \quad if \: x \leq 2 \end{cases}$ Then $f$ is not continuous at x=2 $f$ is continuous and differentiable everywhere $f$ is continuous everywhere but not differentiable at x=1 $f$ is continuous everywhere but not differentiable at x=2 kvkumar asked Jun 2, 2016 edited Oct 11, 2016 by go_editor kvkumar 335 views answer comment Share Follow See all 0 reply Please log in or register to add a comment.
1 votes 1 votes Ans:- A f(2)= 12 RHL= $\int_{0}^{2} {5 + |1-y|} dy$ = 5y + ( y - y$^{2}$/2) sign(|1-y|) = [10 + [2-2]*(-1)] - [ 5*0 + ( 0 - 0)*1] =10 Since F(2)≄RHL F(x) is not continuous at 2. anonymous answered Aug 1, 2016 anonymous comment Share Follow See all 0 reply Please log in or register to add a comment.