`2. lim_(x rarr1)x^2+2x+3`

lim_(x rarr0)(2x^2-3x)/x

If lim_(x rarr 1)((x+x^2+x^3+....+x^n-n)/(x-1))=820 , then find n.

Evaluate : lim_(x rarr1) (logx /(x - 1))

lim_(x rarr0)(1+2x)^(5/x)

7. lim_(x rarr0)(x(log x)^(2))/(1+x+x^(2))

3. lim_(x rarr0)(sin x sin^(-1)x)/(x^(2))

lim_(x rarr 2) (x^6-24 x-16)/(x^3+2x-12)

The value of lim_(x rarr a) (2- a/x)^(tan ((pi x)/(2a))) is:

Evaluate: lim_(xrarr1) ((2x-3)(sqrt(x)-1))/(2x^(2)+x-3)

Let f(x) is a function continuous for all x in R except at x = 0 such that f'(x) lt 0, AA x in (-oo, 0) and f'(x) gt 0, AA x in (0, oo) . If lim_(x rarr 0^(+)) f(x) = 3, lim_(x rarr 0^(-)) f(x) = 4 and f(0) = 5 , then the image of the point (0, 1) about the line, y.lim_(x rarr 0) f(cos^(3) x - cos^(2) x) = x. lim_(x rarr 0) f(sin^(2) x - sin^(3) x) , is