1.if `lim_(x->a)f(x)` and `lim_(x->a) g(x)` both exist , then `lim_(x->a){f(x) g(x)}` exists. 2. If `lim_(x->a){f(x)g(x)}` exists, then both `lim_(x->a)f(x)` and `lim_(x->a)g(x)` exist. Which of the above statements is/are correct ?

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

Consider the following statements : 1. If lim_(xtoa) f(x) and lim_(xtoa) g(x) both exist, then lim_(xtoa) {f(x)g(x)} exists. 2. If lim_(xtoa) {f(x)g(x)} exists, then both lim_(xtoa) f(x) and lim_(xtoa) g(x) must exist. Which of the above statements is /are correct?

1.if lim_(x rarr a)f(x) and lim_(x rarr a)g(x) both exist,then lim_(x rarr a){f(x)g(x)} exists.2. If lim_(x rarr a){f(x)g(x)} exists,then both lim_(x rarr a)f(x) and lim_(x rarr a)g(x) exist.Which of the above statements is/are correct?

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.

If lim_(xtoa) {(f(x))/(g(x))} exists, then

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

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

If lim_(x rarr a)((f(x))/(g(x))) exists,then