`lim_(x-gt0)x(1/(x+h)-1/x)`

lim_(x-gt0) (e^(3x)-1)/(log(1+5x))

lim_(x rarr0)x((1)/(x+h)-(1)/(x))

Evaluate the following limits : lim_(h to 0)1/h[1/(x+h)-1/x]

lim_(x to 0) (2^(x)-1)/(x) +lim_(x to 0) (3^(x)-1)/(x) - lim_(x to 0) ((6^(x)-1)/(x)) equals :

Using lim_(x to 0)(e^(x)-1)/(x)=1 , show that, lim_(x to 0)log_(e)(1+x)/(x)=1

lim_(x->0;)(root(3)(1+3x) \ -1-x)/((1+x)^(101)-1-101 x) has the value equal to

Evaluate the limits, if exist lim_(x-gt0)(log_e(1+2x))/(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