Evaluate :
`lim_( x -> 0 ) ( a^x - 1 - x log_e^a )/x^2`

Evaluate: (lim)_(x rarr e)(log x-1)/(x-e)

Use the formula lim_(x to 0 ) (a^(x) - 1) / x log_(e) a , to find lim_( x to 0) (2^(x)-1)/((1+x)^(1//2) - 1) .

Evaluate: lim_(xto0)(log(e^(x)-x))/(1-cosx)

lim_(x rarr 0) (1+sinx-cosx+log_e(1-x))/x^2

Evaluate : lim_(x rarr e)(log_(e)x-1)/(x-1)

(7) Find the value of lim_(x->0) ((e^(x)-1) log(1+x))/(x^(2))

Evaluate lim_(xto0) (e^(x)-1-x)/(x^(2)).

Evaluate: lim_(x rarr2)(x-2)/(log_(a)(x-1))

Evaluate :lim_(x rarr1)(x^(2)+x log_(e)x-log_(e)x-1)/((x^(2)-1))

Evaluate lim_(x rarr0)(log_(e)x)/(x-1)