Evaluate the limit.

We use this exercise (Section 7.11, Exercise #4) to evaluate,

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Stumbling Robot

A Fraction of a Dot
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Find the limit as *x* goes to 1 of *(1 / log x – 1 / (x-1))*

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2 comments

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I have worked through exercises nr. 6 – 29 and It actually isn’t that complicated. I have one thing however that confuses me and caused some problems (especially at ex. nr. 20 -22). How do I know to what degree I have to take the polynomial? The choices in the solutions sometimes seemed arbitrary to me. I couldn’t see a pattern there. Because of that I sometimes chose to many degrees which resulted in an algebraic mess and sometimes to few degrees which when I evaluated the expression led me back to 0/0 or similiar. Is that something that comes with experience or is there a fixed set or rules that tells me to what degree I have to take the polynomial in each case?

This clearly is trial and error until you get the right expansion. If you do 100 of these, maybe you can easily see the required expansion then.