A Major point which everyone have missed

LHospital Rule can be applied if

(lim x tends to a)f(x)/g(x) where f(x) approach 0 or infinity and g(x) approach 0 or infinity when x approach a respectively

or say we get (0/0) or (infinity/infinity) form

but the functions f(x) and g(x) should be continuous and differentiable at a