(3)` lim_(x rarr1)[2x+3]`

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

3) lim_(x rarr0)[(1)/(x)-cot x]

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

(i) lim_(x rarr0)(x-sin x)/(tan^(3)x)

lim_(x rarr0)sqrt(x)=

If f(x) = sin^(-1) x then prove that lim_(x rarr (1^(+))/(2)) f(3x -4x^(3)) = pi - 3 lim_(x rarr (1^(+))/(2)) sin^(-1) x

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

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

Let a= lim _(x rarr 1) (x/(lnx)-1/(xln x)), b = lim _(x rarr 0) ((x^(3)-16x)/(4x+x^(2))), c= lim _(x rarr 1) ((ln(1+sinx))/x) & d = lim _(x rarr -1) ((x+1)^(3))/([sin (x+1) - (x+1)]) Then [[a,b],[c,d]] is

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