Suneil P. answered • 07/01/14

Knowledgeable and Passionate University of Pennsylvania Math Tutor

Anna R.

asked • 11/27/12Make a proof about definition of limit.

More

Suneil P. answered • 07/01/14

Tutor

5.0
(25)
Knowledgeable and Passionate University of Pennsylvania Math Tutor

I gather you are looking for the epsilon def'n of the limit...

For any ε > 0 you need to find an integer N > 0 so that if n > N then | 1 / n - 0 |< ε---> 1 / ε < n

...so choose N > 1/ε

George C. answered • 11/27/12

Tutor

5
(2)
Humboldt State and Georgetown graduate

1/n, break the numerator and denominator into separate parts. As n—>infinity, the numerator remains unchanged. So we need only to worry about the denominator. The denominator approaches infinity. 1/∞ = 0.

You may also consider L'Hopital's rule. Take the derivative of the denominator, 1 (a constant) and the derivative is 0. Take the derivative of the denominator, n, and it becomes 1. The derivative of the numerator divided by the derivative of the denominator is 0.

Ask a question for free

Get a free answer to a quick problem.

Most questions answered within 4 hours.

Find an Online Tutor Now

Choose an expert and meet online. No packages or subscriptions, pay only for the time you need.

Suneil P.

07/01/14