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## Homework Statement

lim as x[itex]\rightarrow[/itex]-1 = [itex]\frac{|x^{2}-1|}{x^{2}+x}[/itex]

## Homework Equations

N/a

## The Attempt at a Solution

Tried to write this as a piecewise function, but I got lost.

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- Thread starter wvcaudill2
- Start date

- #1

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lim as x[itex]\rightarrow[/itex]-1 = [itex]\frac{|x^{2}-1|}{x^{2}+x}[/itex]

N/a

Tried to write this as a piecewise function, but I got lost.

- #2

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Calculate the right-sided and the left-sided limits separately. That way, you could get rid of those nasty absolute value signs!

- #3

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- #4

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Ok, from the left-hand side of the limit, I got -2, and from the right-hand side I got 2,

The correct solution should be those two switched. From the left side, you should get 2. From the right side, you should get -2. Check your signs.

and when x-1=0 I got "does not exist."

What in earth do you mean with this??

- #5

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I do not see how they should be switched. Can you explain your process in more detail?

- #6

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I do not see how they should be switched. Can you explain your process in more detail?

Well, show your work, and I'll show you what went wrong...

- #7

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- #8

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The absolute first thing you should do is eliminate the absolute value signs around [itex]x^2-1[/itex]. If x comes from the left, then this expression is positive, so you can drop the absolute valuie signs. If x comes from the right, then it is negative, so you'll have to write a minus sign in front.

- #9

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Here is what I have now:

- #10

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Here is what I have now:

Well, if [itex]x\leq -1[/itex], then [itex]x^2-1\geq 0[/itex]. This is easily seen by drawing the parabola for [itex]x^2-1[/itex].

- #11

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- #12

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The parabola is negative between -1 and 1: http://www.wolframalpha.com/input/?i=y%3Dx^2-1

- #13

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