Let `f(x) = {:{(ax^2 +1 , x le1),(x+a ,x>1):}` Show that `underset(xrarr1)Ltf(x)` exists, whatever a may be.

Let f(x) = {:{(|x| for 0<|x|le1), (1 for x = 0):} then

underset(xrarr0)lim (e^x -1)/(x) is equal to

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.

underset(xrarr2)lim (x^3-x^2+1) is equal to:

underset(xrarr0)lim (1-cos2x)/x is equal to:

Prove that underset(xrarr0)lim (a^x-1)/x= log a .

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

if f(x) = {{:(x^2, x le 1),(ax + b ,x gt 1):} is differentiable at x = 1 . Find the values of a and b.

underset(xrarr0)lim (sqrt(1+x)-1)/x is equal to: