Limit of Functions and Tyalor's theorem

[JustinTridums]

Homework Statement

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

Homework Equations

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

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.

 

[VeeEight]

Your image isn't working for me perhaps to explain the problem in text

 

[JustinTridums]

Your image isn't working for me perhaps to explain the problem in text

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

 

[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...

 

[HallsofIvy]

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

 

[JustinTridums]

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...

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!

 

[Tedjn]

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

 

[e(ho0n3]

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