(2) `lim_( x to oo) ( sqrtx+a-sqrtx)`

lim _(h -> 0) (sqrt(x+h) - sqrtx)/h

int (1/sqrtx-sqrtx)dx

y= log(sqrtx+1/sqrtx)

If f(4)= 4, f'(4) =1 then lim_(x to 4) 2((2-sqrtf(x))/ (2 - sqrtx)) is equal to

Let a =lim _(xto0) (ln (cos 2x ))/( 3x ^(2)) , b = lim _(xto0) (sin ^(2) 2x )/(x (1-e ^(x))), c = lim _(x to 1) (sqrtx-x )/( ln x). Then a,b,c satisfy :

lim_(x->oo) (sinx/x) =

lim_(xrarroo) (sqrt(x+sqrt(x+sqrt(x)))) - sqrtx

Evaluate lim_(xto1)(sqrt(x)+sqrt(sqrt(x))+sqrt(sqrt(sqrtx))+sqrt(sqrt(sqrt(sqrt(x))))-4)/(x-1).

Let f is twice differerntiable on R such that f (0)=1, f'(0) =0 and f''(0) =-1, then for a in R, lim _(xtooo) (f((a)/(sqrtx)))^(x)=

lim_(xto oo)(x/(1+x))^(x) is