`lim_(x->0)[(lncosx)/((1+x^2)^(1/4) -1)]`

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

lim_(x->0)((4^x+9^x)/2)^(1/x)

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->0)(1/(x^2)-1/(tan^2x))

Use formula lim_(x rarr0)(a^(x)-1)/(x)=log(a) to find lim_(x rarr0)(2^(x)-1)/((1+x)^((1)/(2))-1)

lim_(x->0) (x^2-3x+1)/(x-1)

lim_(x rarr 0) (2^(x)-1)/((1+x) ^ (1/2) -1) =

Evaluate: lim_(x rarr0)(2^(x)-1)/((1+x)^((1)/(2))-1)