If `("lim")_(xveca)[f(x)+g(x)]=2a n d` `("lim")_(xveca)[f(x)-g(x)]=1,` then find the value of `("lim")_(xveca)f(x)g(x)dot`

If lim_(xtoa)[f(x)+g(x)]=2 and lim_(xtoa) [f(x)-g(x)]=1, then find the value of lim_(xtoa) f(x)g(x).

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)

F(x) is the function such that (lim)_(x->0)(f(x))/x=1\ a n d\ (lim)_(x->0)(x(1+acosx))/((f(x))^3)=1 , then find the value of a

Let f(x)=ax^(3)+bx^(2)+cx+d and g(x)=x^(2)+x-2 If lim_(x rarr1)(f(x))/(g(x))=1 and lim_(x rarr-2)(f(x))/(g(x))=4 then find the value of (c^(2)+d^(2))/(a^(2)+b^(2))

If lim_(x rarr2)f(f(x)+g(x))=2 and lim_(x rarr2)(f(x)-g(x))=1 then lim_(x rarr2)f(x)*g(x) need not exist.

If f(x)=lim_(nrarroo) (cos(x)/(sqrtn))^(n) , then the value of lim_(xrarr0) (f(x)-1)/(x) is

If y=f(x^(3)),z=g(x^(5)),f'(x)=tan x, and g'(x)=sec x then find the value of lim_(x rarr0)(((dy)/(dz)))/(x)

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?

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?