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_> Name: : I, I“ h u ClassmnM Date: IDzD Math 221 - Midterm 1 Se L Multiple Choice
Idennﬁ: the letter of the choice that best completes the statement or answers the question. E 1. The y—coordinate for the midpoint of the line segment joining (2,-4) and (-2,2) is
a. -3 b. 0 ® -1 d. 2 e. None of
these ii 2. The distance between (-2,1) and (3,-4) is a. \l (—2 - 3)2 + (1 + 4)2 c. «l {—_2 +3)2 + (1 — 4)2 e. None of these
b. «I (1 — 3)2 + (—2+ 4)2 d. «h—z + 3): e (1 — 4)2 ﬂ 3. After putting the equation x 2 — 6x + (y + l)2 = 7 into standard form for a circle, we ﬁnd the center has x-coordinate
21. None of b. 2 3 d. -2 e. '-3
these
42; 4. The slope ofthe line through (-2,1) and (2,3) is
a. undeﬁned b. 1/2 c. -l/2 (1. None of e. 2
7 these
481 5. A line perpendicular to 2x + 3y+ 1 = O has slope
a. 2/3 b. 312 c. -3/2 ' d. -2/3 e. None of
these
TV 6. We wish to determine if a given equation deﬁnes y as a function of 2:. To do so, we could
a. Apply the horizontal line test to decide.
b. interchange x and y, then solve for y to see if we get a unique value of y for each value of
x. Ifso, we say yes. Otherwise, we say no.
@ solve the equation for y. Ifwe get a unique value of y for each value of x, we say yes.
Otherwise, we say no.
d. None of these
1
A 7. The function f (x) = + 2 is deﬁned for all real numbers it except
x
a. x=—2 b. x<0 c. x=0 d. x=2 e. Noneof
these
h 8. mm = 2, then f(2) =
a. x b. 2 c. 2x d. 0 e. None of
these
7» _C/_ 9. If f(x) = 4x, and g(x) = 1 , then f (g(x)) =
x +
4x I 4 1
a. b. c. d. e. 7 None of
x + 1 4x + 4 x + I 4x + 1 these ,/ Name:
A? 13.
Refer to exhibit 1-1. Find f (1).
\U a. 0 b. undeﬁned l d. 2 e. None of
these
ﬁ 14. Referto exhibit 1-1. The function f is continuous from the right at x= 1.
G1) The statement is true b. The statement is false
$ 15. Refer to exhibit 1-1. The ﬁmetion f is differentiable at x = 1.
Q2) The statement is false b. The statement is true
i 16. <gefer to exhibit 1-1. The discontinuity at x = l is removable.
The statement is false b. The statement is true
E 2 17.
Find lim 4“ 3.
x-ﬂ 2x -1
a. 0 b. 00 0. None of d. 11/3 e. —00
these 2 18.
2 _'.
Find Iim x 1.
H-I x +1
3.. ‘00 b. 0° c. NOne of thes d. -2 e O
C 19. Find f'(x) if f(x)=‘ 8x5 —x'3 . 40w 4. 5K“
a. 8x 4 — x a c. 40)::4 + 3x -4 e. None of these
to b. 40x4+3x_2 d. 8x4—x"‘
x4 +x2 + 1 73 '4" 1
Pt 20. Find g'(x),ifg(x)=———-—~——. X +X+X 2_ «ix‘i‘i.
x _. X "
2 -2 2
a. 3x +1 -x c. 3x e. None ofthese
3::2 +23: 3
b. —- d. 4x + 2x
x
Short Answer
x — 2 21. List all discontinuities, if any, for g(x) = 2 .
x _ . -55 and ‘b Ode digcmmw‘bﬁg ID: D MATH 221 «1231112002 7 Name\ \’ Midterm #1 — Version A January 31, 2002 Do your work in the space provided. Remember: no work = no partial credit. If you run
out of room on the front, use the back of the page. 1) Find the distance between the following sets of points. Leave your answers in exact
form. 1" ‘5‘ n “h ‘15"? “ﬂ 1
a) (3,-1) and (4,5) 1;) (.L1 and (4’
(H— , . Ki Mere-ﬂ“: 1
1 F M 3» m ’ C: *.\\0
\- 2‘ I ; \"" 2) Find the x— and y-intercepts of the graphs of the given equations:
a) y=3x+15 b) y==x2—8x+15 ,1 lx—l <
f(x)= 3 x J
3x—8 x23 NbJ mas CUW'YYUM d tam—min 1.3" not"
Cchh‘nmems rev AH t‘ﬁ'ﬁll nmth£Vsj bfrﬁixiAg'e
'm m L/A\%§ 4m x, \AEM it?“ r {I} van. ark ‘JL- }
m Baa/ﬂ 1AM Flt/Wt . “this 3% aw E
’h" . "5' 4% at"; (i? \ VFW/\S- (15543 ' Vii";
WOW“? “WM/Maw m Sat/“W, 993% i c to i
4) Let f(x)=-3x+2, g(x =x2—3x+4,and hx)=6.Eva1uatethef ' -
3* a) f (g(x)) b) 11(0) :1 '" 47ml ; “3057‘ 4x143“ "1 \nbd " Y ’ ovi”
Vi = -3 1 mm. um my» .- Emmi. My +q¥mlﬂm we ‘0 WM .n he vAi
i : 'ij'wlx-lp my, . (gin-m4
7 M MW- ._.-,_l.m.~ _ J — ‘ x: D
"a 0) g® ' d) f(x+Ax() I
- l 1,.» ‘ ’ Z -13 >0} Ax 4r
-- i r - « «w
C ’9( 5d?) w
M
ﬁsﬂ—Wx—Mr Mix—kper W Evaluate tile—ionong limit:
. Ail—x2 2+x
‘ f \M (l-VOO/‘VQ *3? 1+7. 1': ;:1(1_X\ % 6) Find the derivative of the following using the limit definition of the derivative: g(x)=:rc2 +x—2 $160 600 z (“A”)? “‘4’” 53‘3'7- * (xiw ~23 “WW :6 7) Let: f(x) = 3x3 — 2x2 ,(E g(x) = 1 h(x) = (3x2 —2)(2x3 +2x—5); and (4302’
6x‘—5 _ ,
MIC): 2 +1. Fmd the followmg:
x
7:
3) f"(x) b) [105) -: Ko-XS + bx?" ~|6x7'— LHC -‘-lx+lo --v x9+LX~5’\5X1-‘+¥+'0‘ “(XV ﬁx? -L+><+| ‘- ‘0 q\
\«> “ W 2.
'3 c) ya) d) gn(0) (7“ 5 s - + , , ‘(x)=—7.(er)'“t -
v (>0- Io(y1 0 (tax 612x) ’5 c ' “WY; @
Lf 1- 4- l '7- .
\ b“ ) 3“va 1+ (LHO
‘*‘ ‘0“ “a ‘ nﬂ‘ox ' = Mfw‘)” = “8:?
($1 .‘ ‘\1 f—_’"_ ______ fwd “ : \oyl-\1xtw\ ‘ ﬁ‘ '
(x7 + .31— ‘V (7'7: lsém 8) Find the equation of the line tangeng function at the given point. Put
your answer in slope-intercept form. f(x)=x3 +2x—5 at (—2,-17) m 3 (IX): gyb?ll
P‘(*2)=Gq-7 U:
\j: W 1'b
: I
7 ﬁ'it‘tb . . . . d
9) Differentiate the followmg unphmtly to ﬁnd :5: b) x2+y3 :6x—2y+3 j “ljoljco . ’Lx Ax wiaTbM-Mj 10) A 25 foot ladder is leaning against a house. The base of the ladder is pulled away
from the house at a rate of 3 ft/s . How fast is the top of the ladder moving down the wall when the base is 24 feet away from the house? 11) The volume of a sphere is changing at a rate of -4 cm3/s. a) What does the negative rate of change mean?
b) What is the rate of change of the radius of the sphere when the radius is 18 cm? W M VD‘uM‘C 0"
is» gmal'mr. 1+ i5 M ‘10“ " 1h Wham-t. -L‘ : U‘V ...

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