**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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