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Unformatted text preview: Limits Worksheet Name By definition, if f ( x ) is continuous at c then lim x c f ( x ) = f ( c ). For most of the functions we encounter in this class, the main obstruction to their continuity at c will be zero appearing in the denominator of a fraction when c is plugged in. So the main tool for evaluating limits will be to algebraically manipulate the function until you get zero out of the denominator. Then you will usually be able to plug c in to evaluate the limit. Here are the most common techniques we will be using: Simplifying Consider lim x x ( x + 3) 3- 27 . First check that we get 0 in the denominator when we plug in 0. Since we also get 0 when you plug in 0 to the numerator, there is hope for this limit to exist (if we ever get d when we plug in, where d 6 = 0, then the limit will not exist, though it could be ). By simplifying ( x + 3) 3 to x 3 + 9 x 2 + 27 x + 27, we get lim x x x 3 + 9 x 2 + 27 x + 27- 27 = lim x x x 3 + 9 x 2 + 27 x = lim x...
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- Spring '09