Evaluate `underset(x to 1)("lim")(underset(k=1)overset(100)(sum) x^(k) - 100)/(x-1).`

Find the value underset(n rarr oo)("lim") underset(k =2)overset(n)sum cos^(-1) ((1 + sqrt((k -1) k(k + 1) (k + 2)))/(k(k + 1)))

Evaluate underset(x rarr 1)(lim) x^((1)/(x-1))

Evaluate underset(x to 0)lim (cosec x - 1/x) .

Evaluate underset(x rarr 0)(lim) (tan^(-1)x)/(x)

Evaluate: underset(x rarr 0)(lim) x^(sin x)

Find the value of underset(r = 1)overset(10)sum underset(s = 1)overset(10)sum tan^(-1) ((r)/(s))

Evaluate: underset(xrarrinfty)lim(1+2x)

Evaluate: underset(xrarr0)lim xlog x

Evaluate underset(x rarr 0)(lim) x^(3) log x