- #1

seasponges

- 16

- 1

The answer is e, but no explanation is given and I cannot figure out why this is. z is undefined in the question.

If anyone could shed some light it would be greatly appreciated.

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- Thread starter seasponges
- Start date

- #1

seasponges

- 16

- 1

The answer is e, but no explanation is given and I cannot figure out why this is. z is undefined in the question.

If anyone could shed some light it would be greatly appreciated.

- #2

Curious3141

Homework Helper

- 2,858

- 88

The answer is e, but no explanation is given and I cannot figure out why this is. z is undefined in the question.

If anyone could shed some light it would be greatly appreciated.

There shouldn't be a z, it should simply be replaced by x.

[tex]\lim_{x \rightarrow 0} {(1 + x)}^{\frac{1}{x}} = e[/tex]

That's actually one of the definitions for e (the base of natural logarithms). If you want a fairly elementary (but not very rigorous) way of proving it, consider putting [itex]y = \frac{1}{x}[/itex], from which you get the equivalent definition:

[tex]\lim_{y \rightarrow \infty} {(1 + \frac{1}{y})}^y = e[/tex]

and apply Binomial theorem to the LHS. Expand and consider the limit as y tends to infinity. Now compare that with the Taylor series for e (e

- #3

seasponges

- 16

- 1

Thankyou very much!

Share:

- Replies
- 32

- Views
- 601

- Replies
- 2

- Views
- 169

- Last Post

- Replies
- 2

- Views
- 256

- Replies
- 26

- Views
- 1K

- Replies
- 4

- Views
- 1K

- Last Post

- Replies
- 9

- Views
- 724

- Last Post

- Replies
- 17

- Views
- 538

- Replies
- 2

- Views
- 254

- Last Post

- Replies
- 14

- Views
- 976

- Last Post

- Replies
- 5

- Views
- 245