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Unformatted text preview: “A [1 17,6 (,1.
Exam 1 M h 408C Name
Fall 2009 TA Discussion Time: TTH
You must show sufﬁcient work in order to receive full credit for a problem. Do your work on the paper provided. Write your name on this sheet and turn it in with your work. Please write legibly and label the problems clearly. Circle your answers when
appropriate. No calculators allowed. Discussing any part of this exam with a classmate who has not yet taken the exam
is considered scholastic dishonesty. 1. Calculate the limits below, if they exist. In the case that a limit doesn’t exist,
indicate whether the limit approaches 00, —00, or neither. You must show sufﬁcient
work to get credit for a correct answer. 1 — 23:
10 ' t l’ (——————)
(a) ( pom S) 221:1; 3 — 5:1: —— 2x2 (b) (10 points) lim t—t—ﬂ t—>1 t—1 4 1
(C) (10 pom) .1311.” + 33) (a? — x + 1) 2. (10 points) Determine whether the function f below is continuous at as = 1. Use
the deﬁnition of continuity to justify your answer. 7r
cos< ), 2:21
Lt—l—l f (15) =
1r — 1 < 1
m
I22 — 1r
1
3. (10 points) Use the deﬁnition of derivative to calculate f’ (x) for f (5r) : 3$ _ 1. (You must use the deﬁnition, not the differentiation rules, in order to get credit for
this problem.) 4. Let y = sin6cos0.
(a)(10 points) Find all values of 0 in the interval [0,27T] where the tangent to the curve is horizontal.
d2
(b) (10 points) Find ﬁt Simplify your answer to a reasonable degree.
5. (10 points) An object moves along a straight line, its position at time t given by t . . . .
803) = for 0 S t, where 8 is measured 1n meters and t 1n seconds. Determine Vﬂ+8 all times t (if any exist), when the velocity of the object is i ft / sec. [MORE ON BACK] 4 tan(a:2) + 1 6. (10 points) Find the equation of the tangent to the curve 3; = + 2
x $20. when mlw 7. (10 points) Find y’ if (:1: + 3/)
degree. : 312:5 + 2. Simplify your answer to a reasonable Bonus (5 points): Calculate the limit below, fully justifying all your steps, or explain
Clearly why it does not exist. lim ;
"H0 sec (i) + a: WW 4331‘ : L” "9% Xa 1,1 3cx—9><" XWz— (I~ax)(3+7<)
.5 i l :1
= — /
3(a); 3+x 3+”; 7'
(L) M Q'T'V't4—3 : QUt4g vQ+\/t43
)(q) t —) X?\ e; *4 91+ v5";
= M L} ~1t+33 )W 1 E
W 3 \ .. = I
t7 a+¥§3 an”? =~—‘;
(C3 JAM. (sz) ( i _. L) ‘ PM" (Xz+x)("
X‘?“ X: 1+! ‘Y‘V"
: JIM» Y(7&+0(‘+¥+‘!¥") _ Q 4%+‘f~x
x—‘a—I y‘lxH) ya—I )c
—_— ’§+‘I—(I)7‘ _ I x4“ {317 M £(K) .: )l/Vv— .35: = M X" .._._. Y‘?’ Yﬁl— Ix~l’ X9! —[x4) 30 M 1:55) M w MES/f M $0 £ ILS We}
Yﬂl MMW J‘Xz,‘ «IA—90 ,a‘
g Q! _.L____ .. __.L_
13,40 3km)" 32M ($(n+h)I)(3x‘)
’33 Md
”1‘40 3x ~I  (SIKHn) a)
4x (3(K+k)~I)/3x~i)
= Xv» 3JA .. 3
Ik—wo ——“——"'——— ._. M m
’2‘ (“M“MVSX") Jae (3(K+k)‘l)(3Xl)
..  3
" f1
(3m 4'. 33WQC¢A9 (“$02, = 3iw9(~S/\8~Q) 1— (>059qu d9
: S~k?9+ws?9
03 .2 z
z s: 34/“ :CpQ
ow 7 9
a #m’Q:
=3 Masjl
:79. 1179, am, “74,704
“’3 a”: _
:13" — 249(‘W79 + c.0293 : — awe m9 «Laws? CWQ) .. ~45~L9m9 ...
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 Spring '06
 McAdam

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