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Exam_II_key - MIDTERM 11 MAT 21A NAME DIRECTIONS Read the...

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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 ’H flM' If}: ‘ 7(— 3 jim- X ~ (X‘lej C ffikl—éo SJQKM 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 ( 11((14 )5 é L( 32% / 7L) 3») (\“fég g0 (211 “(9.?! 1 X.(; . 9 v. a :7 ‘ Z " [Ca ‘ / + a J“ 2. ; 0/ + 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 3% 5%244 3% ’W’ £13, +3 (EC/1L +3 30 *1 (7 214% 1560 7 (’3 fl <50 VH7 3’ WC?) 9 (/H 4311‘ km: (fit/”312 flee/am 9 am um t ”(4‘) 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 :17} L57 50 (WA 11%, ‘ 7r :2 : (km [013!) 9 06-?! ill/L32» Oil? ‘2 33 I ‘ ‘ Mod, {a7 £00 TL 64 we ’32” 9 :0:ka (0%) , 2/ A") 2 1 fit a; {fish 41-- lzlo‘) 2‘ O V 1 (a I’M/Lg], 35' a 9M» ({ka (pi Si 1'- M L09. WCl/V‘L C).<~[‘ § (76) 144491;”??ch S<D % if?" [S Rod/(12a; 1's" {1‘ % mwmmvlfiS ~q© 02 (If) 0/5 5) OZ €311]; [01/th Problem 5: (12 points Find the equation of the line normal to y? = tan—1m at (17 3.25) fl 2‘: {0,31 2 W «1 “ rmJL 17 v I}: 771 (8‘ (M. Cu, ’/ 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 / d3; Mi ;7 4% 1 gay/@174» ,<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, ch, ...
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