lf lim_(x rarr a)((f(x))/(g(x)))_(" exists,then ")

If lim_(x rarr 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.

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

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

1.If lim_(x rarr0)(f(x))/(x) exists and f(0)=0 then f(x) is (a) continuous at x=0 (b) discontinuous at x=0 (e) continuous no where (d) None of these

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

lim_(x rarr5)f(x)=2 and lim_(x rarr5)g(x)=0, then lim_(x rarr5)(f(x))/(g(x)) does not exist.

If f and g are differentiable at a in R such that f(a)=g(a)=0 and g'(a)!=0 then show that lim_(x rarr a)(f(x))/(g(x))=(f'(a))/(g'(a))