{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# lim-know - Some Limits to Know 1 lim x 1 a x x = ea 2 Let k...

This preview shows page 1. Sign up to view the full content.

Some Limits to Know 1. lim x →∞ 1 + a x x = e a 2. Let k be a positive integer and let a > 0 . lim x →∞ x k e ax = lim x →∞ k x k - 1 a e ax = . . . = lim x →∞ k ! a k e ax = 0 3. Let k be a positive integer. lim x →∞ (ln x ) k x = lim x →∞ k (ln x ) k - 1 1 x 1 = . . . = lim x →∞ k ! x = 0 . 4. lim n →∞ n n = lim n →∞ n 1 n = lim x →∞ x 1 x = lim x →∞ e lnx x = e 0 = 1 by #3 5. If c is a positive constant, then lim n →∞ n c = lim n →∞ c 1 n = lim x →∞ c 1 x = lim x →∞ e ln c x = e 0 = 1 6. lim x →∞ a x
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern