Math 1A - Fall 2001 - Vojta - Midterm 1

Math 1A - Fall 2001 - Vojta - Midterm 1 - WED 15:32 FAX...

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Unformatted text preview: 04/24/2002 WED 15:32 FAX 6434330 MOFFITT LIBRARY .001 13- Volta Math 1A First Midterm 50 minutes Fall 2001 1. (16 points) Find the following limits: , 332—5ar+6 _ . rrlazl (at is “gs—4) W .1135 3““ (7 , Ina: . 10 + sinm 00)- .litl— 3573 09- $11.10 m—‘—(1 + sin 33) ((3) lim (lnx)2 + 1 m—+0+ (In :13)2 + 3 2. (6 points) Find , 1 hm 1 , mflm$+ms using only the Squeeze Theorem and other theorems from the book (including limit laws explicitly given in the book, but not informal arguments such as “this is 1oig and that is big, so their product is big”). Explicitly mention those theorems and limit laws that you use. (If you use limit laws, you may give them by name instead of by number, and you do not need to explicitly justify steps from high—school algebra.) 3. (11 points) Find the following derivatives: d 7 g 5_ 3_ i cscx (b). di(zu2emsinmtanm) IL” 4. (6 points) Let éwg if —1 S m S 1; f(:c)= 33—1 if1<m52;and fig H2<m<a Find the intervals where f is continuous, and the intervals Where f is differentiable. Express your answer as concisely as possible, and explain your reasons. (a). Intervals Where f is continuous: (b). Intervals Where f is differentiable: 5. (6 points) Find the following derivative using the definition of the derivative (i.e., using a limit): d. — 2 Gina 1+ :17 6. (5 points) Find the equation of the tangent line to the curve 3; 2 3:4 at the point (2, 16). ...
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