Examine the differentiability of the function `f` defined by `f(x)={2x+3,\ \ \ if-3lt=xlt=-2x+1,\ \ \ if-2lt=x<0x+2,\ \ \ if\ 0lt=xlt=1`

Examine the differentiability of the function f defined by f(x)={2x+3, if -3 <= x< -2, x+1, if -2<=x<0, x+2, if 0<=x<=1

Examine the differentiability of f, where f is defined by f(x) = {(x.[x]",","if " 0 le x lt 2),((x-1)x,"if " 2 le x lt 3):} at x= 2

3. Examine the continuity and differentiability of the function f (x) in (0, 3) where f(x) = { | 2x - 3| [x] ; 0 <=x<=2} and f(x) = { x^2/2 ; 2

Discuss the continuity of the function f, where f is defined by f(x)={{:(3, if0lt=xlt=1),( 4, if1 < x < 3),( 5, if3lt=xlt=10):}

Examine the continuity of the function f defined by f(x)=Lt_(n rarr oo)(x)/((2sin x)^(2x)+1)

A function f (x) is defined as follows : f(x)={{:(2-x",","when "xlt1),(x^(2)-3x",","when "xge1):} Examine the differentiability of the function f (x) at x= 1 , hence state whether f (x) is continuous at x = 1 or not .

Check the continuity of the function f defined by f(x)={{:(x+1,if xle1),(2x,if 1 lt x lt 2x),(1+xA^(2),if x ge 2):} at x=1 and 2

Verify Rolles theorem for the function f(x)=x(x-3)^2,\ 0lt=xlt=3 .