`underset(x→∞)lim(a^(1/x)-1)^(x)`

Value of underset(x to 0)lim (a^(sin x)-1)/(sin x) is

Find underset(x to oo)lim (1+1/x^2)^x

Value of the underset(x to -2)lim (tan pi x)/(x+2)+underset(x to oo)lim (1+1/x^(2))^(x) is

Find the limits : underset(x to oo)lim ((1+x)/(2+x))^((1-sqrtx)//(1-x)) (b) underset(x to oo)lim ((x^(2)+2x-1)/(2x^(2)-3x-2))^((2x+1)//(x-1))

The value of the limit underset(x to oo)lim ((x^(2)-1)/(x^(2)+1))^(x^(2)) equal to

(i) Let h (x) = underset(x to oo)lim(x^(2n) f(x) + g(x))/(1+x^(2n)) , find h(x) in terms of f(fx) and g(x) (ii) without using L Hospital rule or series expansion for e^(x) evaluate underset(x to 0) lim (e^(x) -1-x)/x^(2) (iii) underset(n to oo) lim [ e^(1/n)/n^(2) + 2 ((e^(1/n))^(2))/n^(2) + 3. ((e^(1/n))^(3))/n^(2)+.......+ n((e^(1/n))^(n))/n^(2)] (iv) underset(x to 0)lim[ (a sin x)/x ] + [ (b tan x)/x] Where a,b are inegers and [] denotes integral part. (v) underset(x to a)lim (sinx/sina)^(1/(x-a))