Math151PopSolsII

# Math151PopSolsII - MATH 151 POP QUIZ II: SOLUTIONS REVIEW...

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MATH 151 POP QUIZ II: SOLUTIONS REVIEW FOR CHAPTER 10 Find the following limits. Write or -• when appropriate. If a limit does not exist, and and are inappropriate, write “DNE” (Does Not Exist). 1) lim x x x Æ - - Æ Æ 3 2 9 3 0 0 As x approaches 3, both the numerator and the denominator approach 0. We have the indeterminate form 0 0 at x = 3 . (Indeterminate forms require further analysis on our part.) The “Factoring and Canceling” trick works here. lim lim lim xx x ÆÆ Æ - - = + () - - - π =+ = = 3 2 3 3 9 3 33 3 3 3 3 3 6 We can cancel the factors, because we can assume that if we are considering a limit as approaches 3. We can plug in now. Note: The graph of fx x x () = - - 2 9 3 looks like the graph of gx x 3 , except that there is a removable discontinuity at x = 3 (note that f is undefined there).

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2) lim x x x Æ -- Æ Æ 0 93 0 0 Again, we have the indeterminate form 0 0 . We will do some preliminary manipulation of the given expression; you sometimes have to do this when trig expressions are involved.
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## This note was uploaded on 09/08/2011 for the course MATH 151 taught by Professor Bray during the Spring '07 term at Mesa CC.

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Math151PopSolsII - MATH 151 POP QUIZ II: SOLUTIONS REVIEW...

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