116w08review1 - Review for Exam 1 The first exam covers...

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Review for Exam 1 The first exam covers sections 4.4, 7.8, and 11.1-11.4. In particular, you should know these topics: L’Hospital’s Rule It can be used only on limits that are of the form 0 0 or . The rule says that lim f ( x ) g ( x ) = lim f ( x ) g ( x ) . Other indeterminate forms are 0 ·∞ , ∞-∞ , 0 0 , 0 , and 1 . For the first two, you must use algebra to simplify them into 0 0 or . Taking the natural logarithm of the last three will allow you to rewrite them in the form 0 0 or so that you can apply L’Hospital’s Rule. Improper integrals An integral can be improper for two reasons: because one of the bounds is , or because the function is not defined at some point in the bounds. Replace the offending bound by a new variable, say t , and evaluate the integral as usual. Then take the limit of your answer as t approaches the bound. Sequences A sequence a n converges if lim n →∞ a n exists.
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