Show that `("lim")_(xrarr0)` `(e^(1/x)-1)/(e^(1/x)+1)doe snote xi s t`

Show that lim_(xto0^(-)) ((e^(1//x)-1)/(e^(1//x)+1)) does not exist.

Show that lim_(x rarr0)(e^(x)-1)/(sqrt(1+x)-1)=2

Evalute lim_(xrarr0)((e^(3x)-1)/(x)).

Show that lim_(xrarr0)(1)/(|x|)=oo.

lim_(xrarr0)(pi^(x)-1)/(sqrt(1+x)-1)

lim_(xrarr0) (3sqrt(1+x-1))/(x)

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

Statement 1: If lim_(xto0){f(x)+(sinx)/x} does not exist then lim_(xto0)f(x) does not exist. Statement 2: lim_(xto0)((e^(1//x)-1)/(e^(1//x)+1)) does not exist.

Evaluate lim_(xrarr0) (1+x)^(1/x)

lim_(xrarr0) ((x+1)^(5)-1)/(x)