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Unformatted text preview: Math 16A — 002, Fall 2009.
Nov. 20, 2009. MIDTERM EXAM 2 Instructions: Each' of the ﬁrst four problems is worth 15 points, while problems 5 and 6 are
each worth 20 points. Read each question carefully and answer it in the space provided. YOU
MUST SHOW ALL YOUR WORK TO RECEIVE FULL CREDIT. Clarity of your solutions
may be a factor in determining credit. Calculators, books or notes are not allowed. Make sure that you have a total of 8 pages (including this one) with 6 problems. Read through
the entire exam before beginning to work. . 1
2
3 4
5
6 TOTAL 2 1. Compute the derivatives of the following two functions. Do not simplify! (a)y=(2+x/E)7
a“: 7(2.+1}7<‘1>€. 2‘: X (b) y = x2 .sin(5:z:) 3/: ZX'S'MC5X> + Kl"¢°5(gx> ‘9 3 2. All edges of a cube are expanding (increasing in length) at the same rate. When the volume of the cube is 8 m3, the volume is increasing at the rate of 2 ms/s. Find the rate of the expansion
of the edges at this time. _ 3 43 WW V=€ x22,
x “\f—x 2
iii) ‘3X?’ 3g (M
obt
Pena M ><—2, $1244” M
_ ‘2‘2:
2 49. Our
dx  .1. (WA/5““) (f)
0“; 6 4 3. Find the equation of the tangent line to the curve 2233/2 — y3 + x2 + 3 = O at the point
(You may leave the equation in the pointslope form.) effan flag—bf ~ @3233? *2“ =0
m6 w ><=b 35*”
42 + Ltg‘f ‘ «l3? +l=0
4%= €373 j‘g‘;= 33f;
g
EB 52= EECWU (1,2). 5 4. You are standing on top of a 96 ft tall tower. You throw a rock straight down with velocity 16 ft/sec. How fast is the rock traveling in the moment when it hits the ground? Assume the
accelleration of the rock is constantly —32 ft/sec2. lDGaa‘hmi ,
l &=—4e+,2—%Jc +66 (“l
obt Rock mud:
46} —%+, +5JQ=O ELl'i—ézo 
Gum) Clea) =0 i=1 (“9 Vd/oa‘lz] WM 4 n
\
00
o
a
*5;
\
2
(3
v 3L‘z  4C . . x2 + 1
5. ConSider the function f(:r) —— (x + Dz.
(a) Determine the vertical asymptote of this function and the limits at the vertical asymptote. / ‘)
i r”
._._i M (x)=+ob QM 150=+oo '3‘
x ) “331 + l (3’ z) w
( M414 >0)
(b) Determine the intervals on which y = f is increasing and the intervals on which it is
decreasm/g. _ (XLM) ‘2 (“’0  20Gb (xz+ K _ x2_ 1")
4 ca ’ ——4—~ (x M w
(I l (LAHead ’VLOI‘ I = ~ 4) L (1/ 4:) (c) Determine the horizontal asymptote of this function. 7..
/®‘KM X+4 v/QAME: i x1+2x+l X4” XL (d) Sketch the graph of y = f and determine the range of this function. 3—4iwkruqal1 (0/11,) we X—iM‘iCrceH—(I per pound. You are told that every $0.20 decrease in price, down to price 0, will increase the
number of pounds sold by 4 pounds. Each montly order of Resurrection has a fee of $160 regardless of its size. Each pound ordered
carries a price of $4. (a) Determine the monthly demand function for Resurrection, assuming it is linear. Identify the
proper interval for the order size :3. :0 40 ’F'“ ‘ 243 Cx'éo) y
.64 21.8  (r
13—40 *3 )C + 3 (b) Express your shop’s montly proﬁt P, as a function of m. 2
came + qrx ) Rs x(.,}ox +12) z—zﬁax .+4sx($\
P=u145x1+gx —4Ioo
NW wwwww MM (c) Compute the marginal proﬁt and determine the intervals on which the proﬁt P increases
and decreases. olP____4_
J;— wox +5 (d) Determine the sales level of Resurrecti
and the proﬁt at this sales level. ...
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 Fall '09
 GRAVNER
 Calculus, Mathematical analysis, Limit of a function, Asymptotic curve, WW V=€ x22

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