Q.13quad " If "lim_(x rarr a)((f(x))/(g(x)))" exists,then "

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

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

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?

Lt_(x rarr a)[f(x)+g(x) exists implies dots.

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)

If lm_(x rarr oo)f(x) exists and is finite and nonzero and if lim_(x rarr oo){{f(x)+(3f(x)-1)/(f_(2)(x))}=3 then the value of lim_(x rarr oo)f(x) is ]}

Statement 1: If lim_(x rarr00)(f(x)+(sin x)/(x)) does not exist then lim_(x rarr00)f(x) does not exists. Statement 2:lim_(x rarr o)(sin x)/(x) exists and has value 1.

If lim_(x rarr4)(f(x)-5)/(x-2)=1 then lim_(x rarr4)f(x)=