Prove that `lim_(x->3^+) x/[[x]] != lim_(x->3^-) x/([x])`

lim_(x->0)(3^x-1)/x

If f is an even function, then prove that lim_(x->0^-) f(x) = lim_(x->0^+) f(x)

lim_(x->3)(x^(3)-27)/(x-3)

lim_(x rarr 3)[x] =

lim_(x->0) (x^3-3x+1)/(x-1)

lim_(x rarr3)x+3

8. Prove that lim_(x rarr1^(+))((1)/(x-1))!=lim_(x rarr1^(-))((1)/(x-1))

lim_(x rarr 3)[x] is :

Let f :R to [0,oo) be such that lim_(xto3) f(x) exists and lim_(x to 3) ((f(x))^2-4)/sqrt(|x-3|)=0 . Then lim_(x to 3) f(x) equals