Thursday, August 15, 2019

calculus - How to prove limxtoinftyfracx99ex=infty?





How to prove limxx99ex=0?




I wasn't sure how to do this because both the top and the bottom limits independently turns out to be infinity!


Answer



After successively applying L'Hopital's rule 100 times, you get:




limxx99ex=limx99!ex=0



This is due to the fact that exponentials always grow faster than polynomials. ex will eventually overcome x99.


No comments:

Post a Comment

analysis - Injection, making bijection

I have injection f:AB and I want to get bijection. Can I just resting codomain to f(A)? I know that every function i...