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Unformatted text preview: Name: MA 1021  2006 A Term Section 10
September 7, 2006 Quiz — Sections 1.11.5, 2.12.4, 3.1 1. All students taking MA 1021 in A Term 2006 will take a common ﬁnal exam on Wednesday evening, October 11, 2006, and should
have already cleared their calendar for this time. 01‘ FALSE (please circle the correct answer — 2 points) (x+h)f(x) 2. The slope predictor function is deﬁned as m(x) = f h TRUE 0r(please circle the carrect answer — 2 points)
Inn 3. Students taking MA 1021 in A Term 2006 will have unlimited
chances to pass the Basic Skills component of the ﬁnal TRUE or (please circle the correct answer — 2 points) Per szllabus— 3 Clwtnce: 4.‘ The expression lin’l f (x) denotes a one—sided limit — in this case,
x—>2 the left hand limit of the function f(x) as x approaches 2 from the
left. TRUE or (please circle the correct answer — 2 points) ————— —"— S. x = 3 is a possible solution of the expression: logx 27 = x 1‘ FALSE (please circle the correct answer — 2 points) 6. If = x + 5, g(x) = 2x — 5, and h(x) is the composite of
f(x) and g(x) (denoted by h = f o g), then the graph of h(x) is
a line with slope 2 passing through the origin. r FALSE (please circle the correct answer — 2 points) 7. The line given by f (x) = 3x + 5 is perpendicular to the line given
1 1 by 8(x)="§x—§ 0r FALSE (please circle the correct answer — 2 points) 8. The equation 362 ~— 2x + y2 + 4y — l 7 = 0 describes a circle whose
center is to the right of and below the origin. 01‘ FALSE (please circle the correct answer — 2 points) 9. A ball thrown at an initial velocity of 88 feet/second travels at
approximately the speed of sound. TRUE or lease circle the correct answer — 2 points) 8'3 Ff/sec Q: 60 mph 4 speed 0F Sounol 10. If the righthand limit and the leﬁ~hand limit of a function both exist at x = a , and they are equal to each other, the function is continuous
at that point. TRUE or (please circle the correct answer — 2 points) We aISo require ‘lv exist and Gianni themhrhi'lb) **** End of T rue/False Questions — Quiz Continues on Next Page **** 11. You are given the function f (x) = x2 — 8x +12 A. What are the two values ofx where f (x) =0? (2 points)
B. What is the point where the function crosses the yaxis? (2 points) C. Using the “completethesquare” approach, ﬁnd the xcoordinate and
y—coordinate of the vertex of this function. Note that the general formula for a parabola is given by y — k = a(x — h)2 (2 points) D. What is the equation of the tangent line at the point found in question
[C] above? (2 points) E. Sketch the function. Be sure to label the four points noted in [A], [B],
and [C] above. (2 points) [A3 (x—2)(x—e) 2 0 =>
[:3] 1W0): ll ’X:Z. (IL xcé 12. An opentopped cylindrical can is to be made from cardboard. The can
will have a volume of 50 cubic inches. The bottom of the can will be cut
from a square piece of cardboard, and so some cardboard will be thrown
away (see below). The side of can will be made from a rectangular piece of
cardboard, rolled into shape. Express the surface area of the material required to make this can as a function of the radius of the can’s bottom.
(10 points) Bottom: It takes this ' 1
13. What is the slopepredictor function for: f (x) = — ?
x Use the four step approach described in section 2.1 (and as discussed in
class) — do not use derivatives to solve this! (12 points) £00? l'1) ‘* ((7‘) hm : ﬂ
WM)” la‘PO In
L ,L
I”; X‘HA x
m(x)¢ .__.———*'—"—'_"
mo p
x xsk
Min, Ima sigh)” CHOW“)
, w?" In
LID,“
1 “w CX)(X+M)
fﬁ
W70 L.
. ,— i ._ .ﬂl
: \w s" " '~
h—vo C¥)(xek) x2 14. You are given the following function: f (x) 2 Sketch a graph of the function (10 points) x2—3x—10
x+2 15. Evaluate: 4sin5x lim x—)O 7x Show your work! (5 points) 16. A ball is thrown straight upwards from a point [1 feet above the
ground, at an initial velocity of 64 feet per second. 5 seconds later, it hits
the ground. Note: The general formula for the height of a thrown object is 1 given by: ya) = — gtz + v01 + y0 ,' where g denotes the
2 acceleration due to the force of gravity, which is about 32 ﬂ/Secz. a. How fast is the ball moving at its highest point? (3 points)
b. How fast is the ball moving when it hits the ground? (3 points) 0. Solve for h (4 points) (CL) :15 Lughey} Pot—ml! HM virtual7 (\j 2.24.9 (to) V‘H’): Ldrﬂzl': —31€+ é‘f 237$): Gm“) ’r 4" '3 "3" a5“ ((3 ya): («ta)C§)1+ (9001+ k a o «Hbo't3'zo—liq : 0 ll in»; (0)0 ...
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 Spring '08
 TASHJIAN
 Calculus

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