# Small Limit Problem

• Jun 5th 2009, 08:29 PM
Kasper
Small Limit Problem
Hey, so I have this limit question, and I'm *pretty* sure that the limit does not exist, but I get my back up, because anyone could come to an answer like that from not knowing a way to simplify it. Can anyone see a way to simplify this and get a value?

Thanks for any help!

$lim_{x->1}\frac{x^3+x^2}{x-1}$

Also, sorry for the dumb looking "approaches" arrow in the limit, I couldn't find the code for a good arrow in the LaTeX tutorial. :(
• Jun 5th 2009, 09:18 PM
mr fantastic
Quote:

Originally Posted by Kasper
Hey, so I have this limit question, and I'm *pretty* sure that the limit does not exist, but I get my back up, because anyone could come to an answer like that from not knowing a way to simplify it. Can anyone see a way to simplify this and get a value?

Thanks for any help!

$lim_{x->1}\frac{x^3+x^2}{x-1}$

Also, sorry for the dumb looking "approaches" arrow in the limit, I couldn't find the code for a good arrow in the LaTeX tutorial. :(

$lim_{x \rightarrow 1^+} \frac{x^3+x^2}{x-1} = + \infty$

$lim_{x \rightarrow 1^-} \frac{x^3+x^2}{x-1} = - \infty$

Since the left hand and right hand limits are not equal, the limit does not exist.
• Jun 5th 2009, 10:50 PM
Kasper
Ah right, I was looking at it all wrong. I keep trying to just simplify f(x) to find a way to sub in x and try to algebraically find an answer, I gotta start working on thinking of how the limit approaches rather than trying to find it when it's at the point in question.

Thanks for the clarification!
The text contains a mathematical question about a limit and provides an answer to that question.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# Small Limit Problem

• Jun 5th 2009, 08:29 PM
Kasper
Small Limit Problem
Hey, so I have this limit question, and I'm *pretty* sure that the limit does not exist, but I get my back up, because anyone could come to an answer like that from not knowing a way to simplify it. Can anyone see a way to simplify this and get a value?

Thanks for any help!

$lim_{x->1}\frac{x^3+x^2}{x-1}$

Also, sorry for the dumb looking "approaches" arrow in the limit, I couldn't find the code for a good arrow in the LaTeX tutorial. :(
• Jun 5th 2009, 09:18 PM
mr fantastic
Quote:

Originally Posted by Kasper
Hey, so I have this limit question, and I'm *pretty* sure that the limit does not exist, but I get my back up, because anyone could come to an answer like that from not knowing a way to simplify it. Can anyone see a way to simplify this and get a value?

Thanks for any help!

$lim_{x->1}\frac{x^3+x^2}{x-1}$

Also, sorry for the dumb looking "approaches" arrow in the limit, I couldn't find the code for a good arrow in the LaTeX tutorial. :(

$lim_{x \rightarrow 1^+} \frac{x^3+x^2}{x-1} = + \infty$

$lim_{x \rightarrow 1^-} \frac{x^3+x^2}{x-1} = - \infty$

Since the left hand and right hand limits are not equal, the limit does not exist.
• Jun 5th 2009, 10:50 PM
Kasper
Ah right, I was looking at it all wrong. I keep trying to just simplify f(x) to find a way to sub in x and try to algebraically find an answer, I gotta start working on thinking of how the limit approaches rather than trying to find it when it's at the point in question.

Thanks for the clarification!
user
The text contains a mathematical question about a limit and provides an answer to that question.

TYPE: SINGLE_QUESTION_WITH_ANSWER