Compute `lim_(x->1)sin(x-1)/(x^2-1)`

Compute (lim)_(x->0)(e^(3x)-1)/x

lim_(x->oo)sin(1/x)/(1/x)

lim_(x->2)(sqrt(x-1)-1)/(x-2)

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

If lim_(x->2^-) (ae^(1/|x+2|)-1)/(2-e^(1/(|x+2|)))= lim_(x->2^+)sin ((x^4-16)/(x^5+32)) , then a is

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

Use formula lim_(x->0)(a^x-1)/x=log(a) to find lim_(x->0)(2^x-1)/((1+x)^(1/2)-1)

Evaluate: lim_(x->2)(sin(e^(x-2)-1))/(log(x-1))

The value of lim_(x->0)((sinx-tanx)^2-(1-cos2x)^4+x^5)/(7(tan^(- 1)x)^7+(sin^(- 1)x)^6+3sin^5x) equal to :

If {x} denotes the fractional part of x, then lim_(xrarr1) (x sin {x})/(x-1) , is