Find the limit. Use l'Hospital's Rule if appropriate.  limit as x approaches zero. f(x)=(e^x-1)/(x^5)

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rcmath eNotes educator| Certified Educator

Since `lim_(x->0)e^x-1=1-1=0`  , `lim_(x->0)x^5=0`

and `lim_(x->0)[(e^x-1)']/(x^5)'=lim_(x->0)[e^x]/[5x^4]=1/0`

we can't use l'hopital's rule.

Actually if we look at the graph of the function, we will notice that as x approaches zero, the function tends towards infinity.