Forms for Hospitals

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how can we evaluate the limit as x approaches infinity for this expression x squared over e raised to the x well we could try direct substitution so if we replace x with infinity infinity squared is basically infinity and e raised to the infinity is infinity now this is an indeterminate form what is infinity divided by infinity is it one is it zero is it infinity we don't know so when you get into a situation like this you need to use l'hopital's rule and the basic idea of l'hopital's rule is this the limit as x approaches some number c of f of x over g of x is equal to the limit as x approaches c of f prime of x divided by g prime of x so basically what we can do is turn f into f prime and g into g prime we could do so by taking the derivative of the top and the bottom separately and then maybe we can simplify into a form that we can get the answer so the derivative of x squared is 2x and the derivative of e to the x will remain the same now if we use direct substitution we still won'