If `lim_(x->0^+)f(x)=p and lim_(x->0^-)f(x)=q` then the corrects statement (s) is/are true ?

If lim_(x rarr0^(+))f(x)=p and lim_(x rarr0^(-))f(x)=q then the corrects statement (s) is/are true?

If f(x) =x , x 0 then lim_(x->0) f(x) is equal to

If f(x)=|x|, prove that lim_(x rarr0)f(x)=0

The function f(x) is defined as follows: f(x)=2-3x, when x =0 Evaluate lim_(x rarr0^(+))f(x),lim_(x rarr0^(-))f(x) and hence state whether lim_(x rarr0)f(x) exists or not.

Let f (x) =(ax+b)/(x+1), lim_(x rarr 0)f(x)=2 and lim_(x to oo)f(x)=1 , Prove that f (- 2) = 0.

If f(x)=x,x 0 then lim_(x rarr0)f(x) is equal to

Let f(x) be a continuous and differentiable function satisfying f(x + y) = f(x)f(y) AA x,y in R if f(x) an be expressed as f(x) = 1 + x P(x) + x^2Q(x) where lim_(x->0) P(x) = a and lim_(x->0) Q(x) = b, then f'(x) is equal to :

Let f(x) is a function continuous for all x in R except at x = 0 such that f'(x) lt 0, AA x in (-oo, 0) and f'(x) gt 0, AA x in (0, oo) . If lim_(x rarr 0^(+)) f(x) = 3, lim_(x rarr 0^(-)) f(x) = 4 and f(0) = 5 , then the image of the point (0, 1) about the line, y.lim_(x rarr 0) f(cos^(3) x - cos^(2) x) = x. lim_(x rarr 0) f(sin^(2) x - sin^(3) x) , is

Let f(x) is a function continuous for all x in R except at x = 0 such that f'(x) lt 0, AA x in (-oo, 0) and f'(x) gt 0, AA x in (0, oo) . If lim_(x rarr 0^(+)) f(x) = 3, lim_(x rarr 0^(-)) f(x) = 4 and f(0) = 5 , then the image of the point (0, 1) about the line, y.lim_(x rarr 0) f(cos^(3) x - cos^(2) x) = x. lim_(x rarr 0) f(sin^(2) x - sin^(3) x) , is