[" Given ",(7+4sqrt(3))^(n)=I+F" where "I" is integial pait "],[rArr0

Given lim_(x rarr0)(f(x))/(x^(2))=2, where [.] denotes the greatest integer function,then lim_(x rarr0)[f(x)]=0lim_(x rarr0)[f(x)]=1lim_(x rarr0)[(f(x))/(x)] does not exist lim _(x rarr0)[(f(x))/(x)] exists

Prove that underset (x rarr 0) lim (sin x)/x=1 ,where x is in radian and hence evaluate: underset(x rarr 0)lim (sin 4x)/(sin 2x) .

Find lim_(x rarr 0) f(x) , where f (x) =|x|-5.

If f(x)={x+(1)/(2),x =0 then [(lim)_(x rarr0)f(x)]= (where [.] denotes the greatest integer function)

lim_(x rarr0)(sqrt(x+4)-2)/(x)

If lim_(x rarr 0) (1 + px)^(q/x) = e^(4), where p,q in N , then

lim_(x rarr0)(cos(mx))^((n)/(x^(2))) is : (where m,n in N)

Given lim_(x rarr0)(f(x))/(x^(2))=2 then lim_(x rarr0)[f(x)]=

If lim_(x rarr 0) (1+px)^(q//x) = e^(4) , where p, q, in N, then :

If p= lim_(x rarr0^(+))[(3sin x)/(x)] ,q= lim_(x rarr0^(+))[(3x)/(sin x)] ,r= lim_(x rarr0^(+))[(tan x)/(x)] and s=lim_(x rarr0^(+))[(3tan x)/(x)] where [.] denotes the greatest integer function (A) pqrs=18 (B) pqrs=0 (C) p+q+r+s=9 (D) pq+rs+qr+sp=18