Show that `underset(xrarr0)Lt(1/x)`does not exist.

Prove that : lim_(x rarr 0)(x)/(|x|) does not exist.

Prove that : lim_(x rarr 0) (|x|)/(x) does not exist.

Evaluate underset(xrarr0)Lt [cosx] if it exists. Here [] denotes the greatest integer function.

Find k, so that underset(xrarr2)lim f(x) may exist, where f(x)={(x^2+1, xle2),(x+k, x>2):}

Prove that underset(xrarr0)lim (a^x-1)/x= log a .

underset(xrarr0)lim (1-cos mx)/(1-cos nx) .

underset(xrarr0)lim (sin4x)/(sin2x) is:

underset(xrarr0)lim (e^x -1)/(x) is equal to

underset(xrarre)(Lt)((logx-1)/(x-e)) is equal to

True or False : If underset(x rarr a)Lt f(x)g(x) exists then both underset(xrarra^+)Lt f(X) and underset(xrarra^-) Lt g(x) exist separately.