For `x >0,Lt x^(1/x)+Lt_(x->oo) x^(1/x)=`

For x>0,Ltx^((1)/(x))+Lt_(x rarr oo)x^((1)/(x))=

Lt_(x to 0)x"sin"(1)/(x)=

2. Lt_(x rarr oo)(x)/(1+x)

for x in R,Lt_(x to oo)((x-3)/(x+2))^(x)=

Lt_(x to oo)(x^(n))/(e^(x))=0 for

Lt_(x to 0) ((x-1+cosx)/(x))^(1//x)

Let f(x) lt 0 AA x in (-oo, 0) and f (x) gt 0 ,AA x in (0,oo) also f (0)=0, Again f'(x) lt 0 ,AA x in (-oo, -1) and f '(x) gt 0, AA x in (-1,oo) also f '(-1)=0 given lim _(x to -oo) f (x)=0 and lim _(x to oo) f (x)=oo and function is twice differentiable. If f'(x) lt 0 AA x in (0,oo)and f'(0)=1 then number of solutions of equation f (x)=x ^(2) is : (a) 1 (b) 2 (c) 3 (d) 4

Let f(x) lt 0 AA x in (-oo, 0) and f (x) gt 0 AA x in (0,oo) also f (0)=0, Again f'(x) lt 0 AA x in (-oo, -1) and f '(x) gt AA x in (-1,oo) also f '(-1)=0 given lim _(x to oo) f (x)=0 and lim _(x to oo) f (x)=oo and function is twice differentiable. The minimum number of points where f'(x) is zero is:

Lt_(x to oo)(1+(3)/(x))^(x//2)=