Math 1A - Fall 2000 - Pugh - Midterm 2

# Math 1A - Fall 2000 - Pugh - Midterm 2 - Math 1A Second...

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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 , A3,, L w" ; k, I ,3 _.. It I; i x ' a -2, ﬁiii? cl“, " ‘ L ..w i I i' , v‘ ‘3 " ﬂ 1: ‘ ;- v i \ .. , ” ‘" . ,3 . ‘ L R 1 \/’/M l ~ , I C ya»: :_ (vi) a ”i ix; ! “I x V\:"\ \. i {N I: ‘ ”" f :3 «.347. a} Q i E. , 4- f) t : “if"? I 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. ( ’ \ .., . K W, , (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) ' . ~_ “‘-’ 1 v t , \ 2 w {- i ._ , O K .i ohm ' , “ . ‘ @ C - e il l f ‘ H l 1‘“, W H \ ~— l 6 x ; ihu _ an ( “0°, 0) @ I 1 0 if i \ \ ' ‘ >4, Q 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 '» L V1 ) : \j l K \ i: ”a i wk» ( ‘ V , {'3 i; w ,1 a l H I ' ” >1 r ‘ 1 w , x; - , r *‘l' x / l \\/ \ \\ u, l l , \Z w J ‘ / a 5: 4" {Jig/4 ' t / \‘ .\ "a“ l l \ k ‘ ‘3 of“... " — J ‘ “M. a...“ Jr 2 v » a . v? 1 ~:‘\ \ﬂ " .4- ! i7 f . y r“. avail-kl»: _, L. '3 g3 h,“ r if K ANSWER. ‘ *~ A i): r « ...
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