" 9) "F(x)={[(x^(2))/(2)," if "0<=x<=1],[2x^(2)-3x+(3)/(2)," if "1

Examine the continuity of the function f(x)= {((x^(2))/(2)",","if " 0 le x le 1),(2x^(2)-3x + (3)/(2)",","if " 1 lt x le 2):} at x=1

A function is defined as follows : f(x) = {((x^(2))/(2),"when " 0 le x lt 1),(2x^(2) - 3x + (3)/(2),"when " 1 le x le 2):} Discuss the existence of f'(1).

Check the continuity of f(x) = {{:(x^(2)/2, if 0le x le 1),(2x^(2)-3x+3/2, if 1 lt x le 2):} at x = 1

Discuss continuity of f(x)= {{:(x^(2)/2, if 0le x le 1),(2x^(2)-3x+3/2, if 1 lt x le 2):} at x = 1

If f (x) = {{:((x ^(2))/( 2 ) "," , 0 le x lt 1), (2x ^(2) - 3x + (3)/(2) "," ,1 le x le 2):} then discuss the continuity of f,f'and f'' on [0,2].

Show that the function f given by f(x)= {{:(x^2+2," if "x ne 0),(1," if "x=0):} is not continuous at x=0.

If f(x)={(x^2)/2, if 0<=x<1, 2x^2-3x+3/2, if1 <=x<=2 .Show that f is continuous at x=1 .

If f(x)={(x^2)/2 , if 0lt=xlt=1 2x^2-3x+3/2 , if 1

Let f:RrarrR be function defined by f(x)={(sin(x^2)/2, ifx!=0),(0,if x=0):} Then, at x=0, f is

Examine the following functions for continuity: f(x) = {:{((x^2/2), if 0 le x le 1),(2x^2 - 3x + 3/2, if 1 < x le 2):} at x = 1