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**Unformatted text preview: **Math 1A Second Mid-term Exam November 6, 2000 C. Pugh Closed books, closed notes, no calculators.
Please stay in the exam room until 10.00 am. Except in Problem 1 SHOW ALL WORK. Name
Section 1. (25 points) Answer True or False. +5 for correct answer, —5 for incorrect
answer, 0 for no answer. : VE<.8. { /; 62‘” — 1
‘ The hyperbolic tangent satisﬁes the equation tanhzc = 2/
e I + 1
. d . , t V *
There ex1sts an a: E (0, 1) such that d—((a:(:c — 1) s1n(eI)) = 0
:1: J w a x
As :1: —> oo, / —> oo.
ln(:1;“")
T 1 + le3/2 is an antiderivative of (3/2) ﬁll/2. 2. (25 points) A 52 pound red herring hangs from the end of a rope. The
rope is 60 feet long and passes through a pulley which is 33 feet off the floor.
A man holds the other end of the rope in his hand at a height of 3 feet off the
floor. He runs away from the hanging herring at 5 feet per second. When the
herring is 10 feet below the pulley how fast (in feet per second) is it rising? . ’T" . . 0 w W
Explain. , » \ ~.~ x g/ux “" 53> a
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i r M: {\D 40/2; /‘/ 3. (25 points) Consider the function f (1‘) = 835 — 62 |:1:| -
L_ w k , Maw.“ 3? ”we, . my?)
(a) Find its intervals of increase and decrease, if any. i
(b) Find its local and global extremes, if any. ( ’ \
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(c) Find its asymptotes (vertical, horizontal, and slant) if any. Im’ .
(d) Find its intervals of concavity and points of inﬂection, if any.
(e) Using the data from (a) - (d), graph the function. 6)
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r; r i , 4. (25 points) What is the largest volume of a right Ciregular cone inscribed in a sphere of radius R? Explain. ‘“ ' ' ’ ' ”W lABxféglx'l- ‘1 IQCT
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avail-kl»: _, L. '3 g3 h,“ r if K ANSWER. ‘ *~ A i): r « ...

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