Evaluating a limit-removable discontinuity?

  • Thread starter Thread starter bcjochim07
  • Start date Start date
  • Tags Tags
    Discontinuity
bcjochim07
Messages
366
Reaction score
0
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

 
Physics news on Phys.org


You could use L'hopitals rule.
 


Oh, of course. Thanks. :o)
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
Back
Top