Evaluate` "lim_(x rarr0)3^(x)`

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

Evaluate: lim_(x rarr0)x^(x)

Evaluate "lim_(x rarr0)(x-|x|)/(x)

Evaluate lim_(x rarr0)((a^(x)-b^(x))/(x))

Evaluate lim_(x rarr0)(3x+|x|)/(7x-5|x|)

Evaluate lim_(x rarr0)(x^(3)cot x)/(1-cos x)

Evaluate: lim_(x rarr0)((1-3^(x)-4^(x)+12^(x)))/(sqrt((2cos x+7)-3))

The function f(x) is defined as follows: f(x)=2-3x, when x =0 Evaluate lim_(x rarr0^(+))f(x),lim_(x rarr0^(-))f(x) and hence state whether lim_(x rarr0)f(x) exists or not.

Evaluate lim_(x rarr0^(+))x^(x)

Evaluate lim_(x rarr0)((x)/(sin x))