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

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

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.

Which of the statement(s) is/are incorrect? (A) If f+ g is continuous at x = a, then f and g are continuous at x= a (B) If lim_(x->a) (fg) exists, then both lim_x->a f and lim_(x->a) g exist. (C) Discontinuity at x = a means non-existence of limit. (D) All functions defined on a closed interval attain a maximum or a minimum value in that interval.

If lim_( xto 2 ) (f(x) -f(2))/( x-2) exist ,then

If underset(x to a)("lim")(f(x)-f(a))/(x-a) exists, then

lim_(x rarr a)[f(x)+g(x)]=2 and lim_(x rarr a)[f(x)-g(x)]=1 then lim_(x rarr a)f(x)g(x)