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

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

verify the statement true or false.If lim_( x to a ) [f(x) g(x)] exists, then both lim_( x to a ) f(x) and lim_( x to a ) g (x) exist.

If lim_(x->a)(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

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?