2
$\begingroup$

Can someone help how to compute (step-by-step) the following limit? When I use the online calculator, the answer is -t. However, I do not know how to get that answer.

$$ \lim_{n \to \infty} n (1 - \mathrm{e}^{t/n}) $$

Thanks

$\endgroup$
  • $\begingroup$ All the hints are very useful. I finally understood the method to do by replacing the new variable, such as y = 1/n in the equation. Then, I did one time L^Hopital's Rule. Finally I got -t. $\endgroup$ – user105692 Dec 4 '13 at 3:17
1
$\begingroup$

hint: you can use the Taylor series

$$ e^{t/n} = 1+\frac{t}{n}+\dots \,. $$

$\endgroup$
1
$\begingroup$

HINT: Recall $$\lim_{x \to 0} \dfrac{e^{ax}-1}x =a$$

$\endgroup$
  • $\begingroup$ As we continue to chat here, it is no longer true that only one user has downvoted you more than 5 times. I think that people are reacting badly to your comments about downvoters - though it's hard to say. $\endgroup$ – davidlowryduda Dec 8 '13 at 7:57
  • $\begingroup$ @mixedmath Yes, so all the more reason for the down-votes to be removed. $\endgroup$ – user17762 Dec 8 '13 at 16:37
  • $\begingroup$ @mixedmath Thanks for removing the comment on my post, now time for the down-votes to be removed. $\endgroup$ – user17762 Dec 8 '13 at 20:38

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.