`lim_(x-gt-1)(x^2-x-2)/((x^2+x)+sin(x+1))`

lim_(x->0) (1-cos x)/(sin^2 x)

lim_(x rarr1)(x^(3)+x^(2)-2)/(sin(x-1))

Find the limits (i) (lim)_(x->1)[(x^2+1)/(x+100)] (ii) (lim)_(x->2)[(x^3-4x^2+4x)/(x^2-4)]

lim_(x->0)((1-cos2x)sin5x)/(x^2sin3x)

lim_(x to 0)(e^(2x)-1)/(sin 3x) = ?

Statement-1 : lim_(x to 0) (1 - cos x)/(x(2^(x) - 1)) = (1)/(2) log_(2) e . Statement : lim_(x to 0) ("sin" x)/(x) = 1 , lim_(x to 0) (a^(x) - 1)/(x) = log a, a gt 0

Statement-1 : lim_(x to 0) (1 - cos x)/(x(2^(x) - 1)) = (1)/(2) log_(2) e . Statement : lim_(x to 0) ("sin" x)/(x) = 1 , lim_(x to 0) (a^(x) - 1)/(x) = log a, a gt 0

lim_(x to 0) (x +2 sin x)/(sqrt(x^(2)+2 sin x + 1)-sqrt(sin^(2) x - x+ 1)) is

lim_(x to 0) (e^(x^2) - 1)/sin^2x