Evalute
(i) `underset(x to 1)(lim) [(x)/(2)]` (ii) `underset(x to 2)(lim) [x^(2) - 5]`

Evaluate underset(x to oo) lim ([x])/(2x)

Evaluate underset(x to oo) lim ([x])/(2x)

underset(x to 0)lim 2 (sqrtx)=

underset(x to 1)lim (1-x) tan(pix//2) =

underset(x to -2)lim (tan pix)/(x+2)+underset(x to oo)lim (1+1//x^(2))=

Find (i) underset(x to 5)(lim 6) (ii) underset(x to 2)(lim x) (iii) underset(x to 3)(lim [x + 2]) (iv) underset(x to 2)(lim 4x + 2])

Find (i) underset(x to 5)(lim 6) (ii) underset(x to 2)(lim x) (iii) underset(x to 3)(lim [x + 2]) (iv) underset(x to 2)(lim 4x + 2])

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

(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))