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

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

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

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

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[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,

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

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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?

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

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

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

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

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