SOLUTION: Please explain how to solve this limit problem
lim ->0 (e^x-1)/x
I know my teacher gave the answer as 1 but I didn't understand. Could you please give details on how this is
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Question 986568: Please explain how to solve this limit problem
lim ->0 (e^x-1)/x
I know my teacher gave the answer as 1 but I didn't understand. Could you please give details on how this is solved.
Thank you
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
I'm going to assume you mean
because
doesn't exist (the limit from the left is 
and the limit from the right is 
)
Since 
we have the L'Hôpital indeterminate form 
. Since it is a proper indeterminate form, we can use L'Hôpital's Rule: evaluate the limit of the derivative of the numerator over the derivative of the denominator.
}{\frac{dx}{dx}}\ =\ \lim_{x\right 0} \frac{e^x}{1}\ =\ \frac{e^0}{1}\ =\ 1)
John
My calculator said it, I believe it, that settles it
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