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Unformatted text preview:  Math 171
’ Fall 2007» 3
4
I 5
7 Exam *2 . C. Gomez
November 15, 2007 ‘ Name:
TA’s Name Discussion Section Time This exam contains 10 pages, and 7 prob—
lems. Before you begin, please make sure
all the pages are here. No calculators, notes, or books are allowed.
The last page contains Some geometric for—
mulas that you may or may not need. If
you decide to remove that page, please do
so carefully. You must show all your work, and ex:
plain your reasoning to receive credit
for your answers. ' Be sure to check your answers whenever pos . sible. When you are ﬁnished, please return your
exam to your TA. Good luck! Math 171 Exam 2 ' 1.‘ Evaluate the limit or explain Why it does not exist. . . [x1
(a) [5 pomts] 933%; a: (b) [5 points] Iim i— x—woo t — 5 Math 171.Exam 2 1. (continued) ' (c) [5 points] lim 2m + 1 m—wo m 93900 ((1) [5 points] lim (m  cc) NbﬁlflﬁmmZ , ' 4 2. [10 points] Find the values of a and b so that the following function is continuous
everywhere. x+L ﬁm<1
.ax+b, iflgac<2
3x, ifafZQ Math171Exam2 , . , V» .5 3. (a) [5 pOints] Use the deﬁnition of the derivative to ﬁnd f’ (4), where f (3:) = i (b) [5 points] Use your answer to part a to ﬁnd an equation for the tangent to .
y =f(:c) at x = 4. a:
53—5 . (c) [10 points] Use the deﬁnition of the derivative to ﬁnd g’ (x), Where g(:v) =  Math 171 Exam 2 4. Find the indicated dérivative. (a) [5 points] £;[3x($3 _ 1)] (b) [5 poirits] f”(m), where f (IE) = (jg—:11) . d?! 3—, Where y is implicitly deﬁned by 3033/ + y3x = 30.
a: V (c) [5 points] Math 171 Exam 2 7 .2 .— V
5. [12 points] Sketch the graph of y = a: 9, labeling all intercepts and asymptotes. {133—35 Math 17] Exam 2 l l 8 6. [10 points] An object thrown vertically downward from the top of a cliff with initial
velocity 210 feet per second falls approximately 3' =_v0t + 16752 feet in t seconds.» If
it strikes the ocean below in 3 seconds with avelocity of 140 ft/s, how high is the
cliﬁ? , Math 17] Exam 2 ‘ g 9 7. [13 points] Water is pouring into a conical tank at a rate of 8 cubic feet per' minute.
If the height of the tank is 12 feet and the radius of its circular opening is 6 feet,
how fast is the water level rising When the water is 4 feet deep? Math 171 Exam 2 Formulas You May or 'May Not Need Geometric Formulas volume of a cone: V = §7rr2h surface area of a cone: 5’ = 7rrx/r2 + h2
volume. of a sphere: V = §7rr3
surface area of a sphere: S = 47W"2 volume of a right circular cylinder: V = 7rr2h surface area of a right circular cylinder:
5' = 27rrh 10 ...
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 Fall '07
 GOMEZ,JONES
 Calculus, Algebra, Trigonometry

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