Test differentiability of the following function at the indicated points.
`f(x)={(1-2x,xle1/2),(x-1/2,x>1/2) :} at x=1/2`

Test differentiability of the following function at the indicated points. f(x)=[x^2+1]at x=-1/2

Test differentiability of the following function at the indicated points. f(x)=x+|cosx|at x= pi/2

f(x)={(1-x, x le1/2),(x,x gt 1/2):} at x=1/2

Examine the continuity of the following functions at the indicated points: f(x) = {(x+1/2,xle1/2),(3/2-x a,xgt1/2):}at x=1/2

Examine the continuity of the following functions at indicated points. f(x)={(1/(x+[x])ifxlt0),(-1 if xge0):}

Examine the continuity of the following functions at indicated points. f(x)={((x^2-1)/(x-1)ifxne1 at x=1),(2if x=1):}

Examine the contiunity of the following functions at the indicated points . f(x) = {[2x+1 ,if xle0],[x, if 0 < x < 1],[2x-1,if xge1]:} at x=0,1.

examine the contiunity of the following functions at indicated points . f(x) = {[(1+2x)^(1/x)if x!= 0],[(e^2)if x=0]:} at x=0 .

Test differentiability and continuity of the following functions. |1-1/x| at x = 1

Examine the continuity of the following functions at indicated points. f(x)={(1/(e^(1/2)-1)ifxgt0 at x=0),(0 if xle0):}