Let `f(x) = {:{(x^2,xge0),(ax,x<0):}`. Find Lf'(0) and Rf'(0) and hence, find the value of 'a' for which f is derivable at x = 0.

Find a in R so that f(x) = {:{(x^2, x ge0),(ax,x<0):} is continuous at 0.

Let f(x) = {:{(2x-5,if xge2),(x^2, if x <2):} . Is f continuous at x = 2?

Determine the constants 'a' and 'b' so that the function 'f' defined below is continuous everywhere: f(x) = {:{(x+2,xle2),(ax+b,2 < x<5),(3x-2,xge5):}

Let f(x) = {:{(ax+3,xle2),(a^2x-1,x>2):} . Then the value of 'a' for which 'f' is continuous for all x are

Let f(x) = {:{(x+a, x le1),(ax^2 + 1, x > 1):} . Show that f is continuous at 1. Find 'a' so that it is derivable at 1.

True or False : The function f(x) = {:{(x+a, xge1),(ax^2 +1, x <1):} is continuous at x = 1, whatever 'a' may be.

Let f(x)= {(cosx,if, xge0),(x+k,if, x<0.):} Find the value of the constant k, given that lim_(x rarr 0) f(x) exists.

If f(x) = {:{(kx^2,x <2),(3,xge2):} is continous at x =0, the value of 'k' is

Discuss the continuity of the function f(x), where f(x)= {:{(2-x, x < 0),(2+x,xge0):} , at x = 2,0 and -2.

Examine the following functions for continuity: f(x) = {:{(x+a,x<1),(ax^2+1,xge1):} at x = 1