Limit of a function `f(x)` is said to exist at, `x->a` when `Lim_(x->a) f(x) = Lim_(x->a)f(x)` = Finite quantity.

If function f(x) is differentiable at x=a , then lim_(xtoa)(x^(2)f(a)-a^(2)f(x))/(x-a) is :

If f is an even function, then prove that lim_(x->0^-) f(x) = lim_(x->0^+) f(x)

A function f is said to be removable discontinuity at x = 0, if lim_(x to 0)f(x) exists and

If lim_(x->a)[f(x)g(x)] exists, then both lim_(xtoa)f(x) and lim_(x->a)g(x) exist.

If f is an even function , then prove that Lim_( xto 0^(-)) f(x) = Lim_(x to 0^(+)) f(x) , whenever they exist .

If f(x) is an odd function and lim_(x rarr 0) f(x) exists, then lim_(x rarr 0) f(x) is

Which of the following statement(s) is (are) INCORRECT ?. (A) If lim_(x->c) f(x) and lim_(x->c) g(x) both does not exist then lim_(x->c) f(g(x)) also does not exist.(B) If lim_(x->c) f(x) and lim_(x->c) g(x) both does not exist then lim_(x->c) f'(g(x)) also does not exist.(C) If lim_(x->c) f(x) exists and lim_(x->c) g(x) does not exist then lim_(x->c) g(f(x)) does not exist. (D) If lim_(x->c) f(x) and lim_(x->c) g(x) both exist then lim_(x->c) f(g(x)) and lim_(x->c) g(f(x)) also exist.

If ("lim")_(x->a)[f(x)g(x)] exists, then both ("lim")_(x->a)f(x)a n d("lim")_(x->a)g(x) exist.

If ("lim")_(x->a)[f(x)g(x)] exists, then both ("lim")_(x->a)f(x)a n d("lim")_(x->a)g(x) exist.