`2. lim_(x rarr1)(3)/(2x+5)`

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

1) Evaluate lim_(x rarr0)(|x|)/(x)

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

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

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

lim_(x rarr oo)e^(-x)x^(2)

lim_(x rarr1)(1)/((x-1))((1)/(x+3)-(2)/(3x+5))

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

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

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