text: # 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!
explanation: The document is a forum post and response discussing a limit problem in calculus. The original poster (Kasper) presents a limit question and expresses uncertainty about whether the limit exists. The responder (mr fantastic) confirms that the limit does not exist by evaluating the left-hand and right-hand limits, showing they are not equal. Kasper then acknowledges the response and reflects on the approach to solving such problems.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: # 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!
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document is a forum post and response discussing a limit problem in calculus. The original poster (Kasper) presents a limit question and expresses uncertainty about whether the limit exists. The responder (mr fantastic) confirms that the limit does not exist by evaluating the left-hand and right-hand limits, showing they are not equal. Kasper then acknowledges the response and reflects on the approach to solving such problems.
  
  Label: question-and-answer