. If `lim_(x->c) (f(x)-f(c))/(x-c)` exists finitely, then1) limf(x) = f(c) 2) limf (x) = f(c)3) limf(x) does not exist4) limf(x) may or may not exist

If (lim)_(x->c)(f(x)-f(c))/(x-c) exists finitely, write the value of (lim)_(x->c)f(x) .

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

If (lim)_(x rarr c)(f(x)-f(c))/(x-c) exists finitely,write the value of (lim)_(x rarr c)f(x)

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

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

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.

If f(x)=(|x-1|)/(x-1) prove that lim_(x rarr1)f(x) does not exist.

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.