please help me to solve that

Results 1 to 9 of 9

- October 26th 2006, 02:37 AM #1

- Joined
- Jul 2006
- Posts
- 95

- October 26th 2006, 03:34 AM #2

- Joined
- Nov 2005
- From
- someplace
- Posts
- 14,972
- Thanks
- 4

- October 26th 2006, 06:15 AM #3

- Joined
- Oct 2006
- Posts
- 7

- October 26th 2006, 07:36 AM #4

- Joined
- Nov 2005
- From
- New York City
- Posts
- 10,616
- Thanks
- 10

[QUOTE=ThePerfectHacker;25185]Question 1, Use the standard rationalization trick,

The function,

And,

Agree for sufficiently large , thus the limits are the same.

Working with the second function we find,

Thus,

For suffiently large, i.e., we factor,

Factor again,

Thus,

Now,

limit compositions rule,

Thus, by limit composition rule again,

- October 26th 2006, 10:08 AM #5

- Joined
- May 2006
- From
- Lexington, MA (USA)
- Posts
- 11,914
- Thanks
- 779

Hello, m777!

A slightly different approach to #1 . . .

Multiply top and bottom by

. .

Divide top and bottom by

Take the limit: .

~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~

Did you make a sketch?Code:| | (a,2a) | o * * * * * * | * | * | * *(a,a) * | --------+-------+--------------- - | a

Rather obvious that it's discontinuous at , isn't it?

- October 26th 2006, 10:20 AM #6

- Joined
- Nov 2005
- From
- someplace
- Posts
- 14,972
- Thanks
- 4

- October 26th 2006, 10:32 AM #7

- October 26th 2006, 10:42 AM #8

- Joined
- Nov 2005
- From
- New York City
- Posts
- 10,616
- Thanks
- 10

- October 26th 2006, 11:29 AM #9

- Joined
- Jul 2006
- Posts
- 95