[" Giver ",(7+4sqrt(3))^(n)=I+F" where "I" is integial pail "],[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) .

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)

If I_(1)=lim_(x rarr0^(+))(sin{x})/({x}) and I_(2)=lim_(x rarr0^(+))(sin{x})/({x}), where {.} denotes the fractional function,then

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

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

The function f(x) is defined as follows: f(x)=2-3x, when x =0 Evaluate lim_(x rarr0^(+))f(x),lim_(x rarr0^(-))f(x) and hence state whether lim_(x rarr0)f(x) exists or not.

lim_(x rarr 0) x/(sqrt(x+4)-2) =