This preview shows pages 1–6. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Math 123 CalculusI Name: jobmo/Uﬁ  ﬁrm Exam I Fall 2007 RWJ
No calculators allowed, one page of notes allowed Instructions:
0 Read questions carefully 0 Help me award you (partial) credit by showing your work (except on problems 4
and 5) 0 Note point values on questions — 105 points are listed, 1 00 points is possible
0 Check your answers you ﬁnish early
0 The exam ends promptly at 2:5;
0 Good luck! 1 / 2 8 2 / l 5 3 / 2 O 4 / l O 5 . / 8 6 / 9 7 . / l 5 /105 1. (28 pts.) Compute the derivatives of the following. Don ’t waste time simplz‘ﬁ/ing.
a. 5x7 +3x3 —6x—10 95%cJ' 7762— e b (5x6 + 2x4 —7x2 +x+3)sinx (30x5+3w3—I+x+) 5.4;): 4_ [5Ké*2x¢'7x1+‘7c+3) (o x W
2x3 +x—5 (5W5 7*” Haw 7%) » (whawh wwzaam)
MW ( twg‘t'wc—é')?‘ C. d. tan[(x2 +5x+3)“2] —//
klfo'z‘ +§x¢3)’"3: é(7c"k2;,r+g) 3' [27‘ +5) 2. (15 pts.) The position of an object at time x is given by f(x)=\/x+3 a. Find the position of the object at time x =1. Also ﬁnd the position of the object at time x = 6.
PM = J7 =69
r9 [6) :ﬁ :1 b. What is the average velocity of the object over the time interval [1,6]?
Q/é),P/)) 31 = L
K— 1 2:7 ; c. Give an expression for the average velocity over the time interval [x, x + h]. XIXM) Plx) _. \i'xrkk}  Jx+3 In .. ________________. (1. Using your answer from part c (and not any “shortcut” methods) determine the
instantaneous velocity of the object at time x. [70,“) , (70,} m 447“) : (7;+Lar3)~—(7u3)
14 m +‘1m3 la [ 79:46 hi x43)
1 ________________._. (m 4"] war?) ll glxkh)  IF/w) A
M; I _,__l___
=ﬂf'zt2’3 441
J; J
,7
Jx 3. (20 pts.) Find Don’t waste time simplifying.
x x2 sinx a. =
y x3+2x+3 ._ (zﬁﬁnk XIMW)(K3+7—xr3) ’— (7679‘; ,C')(3?(1+_7_ [ngzx f 3)1
b. y = (8x3 + 6x+ 5)3(x2 +3x+2)10 , 5/3K34’éxi5)7(2+w‘+ 4)('X1vf'37:+1) ” +
(5X9*4°<*'5)9 /0 {KW37:41,)? ﬁnd» 3) 92 will be in terms of both x and y) c. 2xy2 = sin(xy) (your expression for d
x 1. J 
jig—*7] = J; Raw»)
zflfgﬁ)»'xj£,71 : 410—037)'j:[K0)
.J
,L (71., x27 : Mbwy) . [LU/7+ 'K ify (kc? ' qCMJW») , gm/KO)’ 7"‘7
42¢ m é: 1x ’ 4X7'7Cm’hp7) 4. (10 pts.) For each of the following indicate whether the statement is true or false (no
work necessary): a. If f is not continuous at x, then f is not differentiable at r False (circle one)? b. If f is continuous at x, then f is differentiable at x. True o@ircle one)? X)C c. For any function f, lim f (x) = f (c). True 0@e/(circle one)? (1. If f and g are differentiable, then (f + g) '= f '+ g ‘ @r False (circle one)? e. If f and g are differentiable, then (fg)‘ = f ' g'. True or @ircle one)? 5. (8 pts.) Fillin the blank: a. If lim f (x) = f (c), then we say that f is (VP 7710004)} at c. X—>C b. If f '(x) exists, then we say that f is p/FFW W“:— at x. 6. (9 pts.) Suppose f is a continuous function on [2,8]. Also suppose f(2)=3
f(8)=7 ff.
a. f necessarily has a zero (or root) between what two x values? 4—H—‘i— 2 a2 7— 5
b. If the bisection method is used, at what x value do we now evaluate f?
2 + S’ ' "
7. (a
. Suppose f is positive at the x value you gave in p . ere do you now evaluate j?
‘33.
\
(K .
L pltp ,a
O? l.
C'lv p W
W 7. (15 pts.) For the following limit problems:
0 If the limit exists, give me the (ﬁnite) value of the limit 0 If a limit does not exist, answer using 00 or —00 when appropriate, otherwise
write “Does Not Exist” \ b limx2+4x+l _ (Daur 710*] _ ,5 £72.)
. x—>1 x+2 3 ...
View
Full
Document
This homework help was uploaded on 01/22/2008 for the course MATH 123 taught by Professor Johnson during the Fall '06 term at SDSMT.
 Fall '06
 JOHNSON
 Calculus

Click to edit the document details