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Unformatted text preview: MIDTERM 11 MAT 21A NAME: DIRECTIONS: Read the directions carefully before beginning. Good Luck! 0 This exam is a closed book, closed notes. Nothing should on the table except a pencil. an eraser, and
this exam. 0 NO CALCULATORS or other PAPERS allowed. 0 Show all work, clearly and in order. I When required, do not forget the units! a Circle your ﬁnal answers. You will loose points if you do not circle your answers. 0 This test has 7 problems, one extra credit problem, and 6 pages, It is your responsibility to make sure
that you have all of the pages! Question l Points Score LU Extra Credit 10
l— Total 90 MIDTERM II MAT 21A NAME: Pg? Problem 1: (10 points) Using the deﬁnition of a derivative (limh_>oﬂi’ihhtf—m), ﬁnd the derivative of NC) = l. i
a: + 2 I V «I
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u, ‘ .50 ET). haw ,> L”) hm It ' K +1 Problem 2: (woints) Find the derivatives of the following. (a) (6 points) 1%) = sfigﬁy 7/ it §a32 523‘ (kn) *“2Q§(x+‘l®
M ' PZ/ +L. MIDTERM 11 MAT 21A NAME: [(1% Problem 3: (18 points) You throw a ball straight up in the air with an initial velocity of 64 ft/sec. The
height of the ball is given by h(t) = 64t  16t2. (a) (6 points) What IS the maximum height attained by the ball (1 e. when is the tangent line horizontal)? (DON’T FORGET YOUR UNITS ) //~\‘ {4? 1% l: ( V (
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+ 2/ (b) (12 points) What IS the velocity speed and acceh ration when the ball IS on its way up and is at a height
4 30f the maximum? (DON’T FORGET YOUR UNITS.) f“ WW. ﬁlm/[n 3. (/7
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11—» (l MIDTERM II Problem 4: (12 points) MAT 21A NAME: b a? Parametrize the minute hand of a clock as it moves over a one hour interval from the 12 back around to the 12 with time t such that (I < t < 60 ZIT X2 0
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Problem 5: (12 points Find the equation of the line normal to y? = tan—1m at (17 3.25)
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’/ J V YO {3 ,— MIDTERM II MAT 21A NAME: kg} i‘ Problem 6: (14 points) A toddler lets go of a party balloon which starts to ﬂoat straight up. Suppose the
height of the balloon is given by y. The balloon is being watched by a squirrel 50 feet away from the toddler.
When the angle of sight for the squirrel, 0, is 6 = $6 is increasing at a. rate of 0.1 radians/ minute (i.e., when 6 = g, % = 0.1). How fast is the balloon rising at this time (i.e.7 what is %%), when 0 = g? (DON’T FORGET YOUR UNITS.) :5? : his => ﬂsfodmﬁg
o) MIDTERM II MAT 21A NAME: ICE ;? Problem 7: (12 points) Find the equation of the tangent line to the ellipse parametrized by a:(t) 2: cost y(t) 2 23m withOStS27rattzg. I i /
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,<4Y27{ " £ ~ Extra Credit 1: (10 points) Find the delivative of f ( ') = x35“ 71”) and explain any restrictions on x. /
I“ 33“ X ~/
‘R/O =‘ xzm QC?) QW’ t. 32am ux WﬂﬂncbénMg (V5, XWQFIK 2X HAL (£917an d. 3m,
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 Spring '07
 Osserman

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