# Limit of Functions and Tyalor's theorem

1. Dec 3, 2008

### JustinTridums

1. The problem statement, all variables and given/known data
The problem is attached with this message.
Here is the direct link of the image: http://picasaweb.google.ca/lh/photo/8QB5XydAGZP4jIXfej9lsw?authkey=x-xog63oZxw [Broken]

2. Relevant equations
for problem B I know I need to use Taylor's theorem. But I am not sure how to get started?

3. The attempt at a solution

For problem A I think I need to assume 1/x=y and the y-> infinity, is this right direction?

BTW Tan represents the principle branch of tangent function.

#### Attached Files:

• ###### Problem.JPG
File size:
30.1 KB
Views:
47
Last edited by a moderator: May 3, 2017
2. Dec 3, 2008

### VeeEight

Your image isnt working for me perhaps to explain the problem in text

3. Dec 3, 2008

### JustinTridums

updated the message, there is adirect link to the image now.
Thanks.

4. Dec 4, 2008

### gabbagabbahey

For part A, you should know that $\tan^{-1}(+\infty)=\frac{\pi}{2}$, so your limit is of the form $\frac{0}{0}$ and you can use l'Hopital's rule.

For B;if f'(x)=f(x), then f''(x)=__? And so f'''(x)=__?And so.....

5. Dec 4, 2008

### HallsofIvy

Staff Emeritus
This clearly is not "pre" calculus so I am moving it to "Calculus and Beyond".

6. Dec 4, 2008

### JustinTridums

I got part a abd b of part B but now I am stuck at proving that it is bounded by [0,x] and after that I think I know. But if you can help me with that that would be great!

7. Dec 4, 2008

### Tedjn

What does it mean for f(x) to be bounded on [0,x]?

8. Dec 5, 2008

### e(ho0n3

It means there exists a value M such that |f(y)| ≤ M for all y in [0,x].