Evaluating a limit-removable discontinuity?

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SUMMARY

The discussion centers on evaluating the limit of the vector-valued function ln(t)/(t^2 - 1) as t approaches 1, which presents a removable discontinuity. The user graphed the function and observed that the limit appears to be 0.5. The solution involves applying L'Hôpital's Rule, a technique used to resolve indeterminate forms in calculus. This method is essential for finding the limit when direct substitution leads to an undefined expression.

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  • Understanding of limits in calculus
  • Familiarity with removable discontinuities
  • Knowledge of L'Hôpital's Rule
  • Basic graphing skills for functions
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  • Study L'Hôpital's Rule in detail
  • Practice evaluating limits involving removable discontinuities
  • Explore vector-valued functions and their limits
  • Review techniques for graphing functions and interpreting their behavior
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Students studying calculus, particularly those focusing on limits and discontinuities, as well as educators seeking to clarify concepts related to L'Hôpital's Rule and vector-valued functions.

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evaluating a limit--removable discontinuity?

Homework Statement


I am evaluating the limit of a vector valued function, and one of the pieces I must evaluate is the limit as t approaches 1 of ln(t)/(t^2 -1). I graphed this function on my calculator, and it seems to me that there is a removable discontinuity. However, the expression cannot be factored so terms will cancel out. If I move the cursor around on my calculator, it also appears that the limit is 0.5, but I'm not sure how to obtain that. It's been awhile since I took Calc. I, so could somebody please help me out? Thanks.

Homework Equations





The Attempt at a Solution

 
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You could use L'hopitals rule.
 


Oh, of course. Thanks. :o)
 

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