Midterm 2 Solution

Midterm 2 Solution - Q1 (20 pts) Last Initial Q2 (20 pts)_...

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Unformatted text preview: Q1 (20 pts) Last Initial Q2 (20 pts)_ Section Q3 (20 pts)__ Full Name Q4 (20 pts)_____ Student ID # Q5 (20 pts)_ 2 MIDTERM EXAMINATION 21A §B01-04, 10:00-10:50 am Friday November 6, 2009 Show your work on every problem. Correct answers with no support- ing work will not receive full credit. Be organized and use notation ap- propriately. Please write legiblyl! Crossed out answers will not receive credit. Declaration of honesty: I, the undersigned, do hereby swear to uphold the highest standards of academic honesty, including, but not limited to, submitting work that is original, my own and unaided by notes, books, calculators, mobile phones, or any other electronic device. You should have only a pencil and eraser on your desk. Signature Date 2 Question 1 (20 points) Find an equation for a line that is tangent to the graph y 2 6I and goes through the point (—1, —e). W", 79;“ng [We QJ/Oomnz a {1/ fix, Wm «M w a a = (a) + {ha/Wot) z ea + 9‘60” 01" 6:35 77» 5044 429w ¥a 6’7émlfit9m 5) £13 “I! :7 W{x«z)= ext WW .. WW 3 Question 2 (20 points) Using the rules we learned in class (such as the sum, product, quotient, chain rule), and the derivatives of :c" for integers n, 008(55), sin(:r), and ex calculate the following derivatives: (a) 2 (If _ . I “ 1+Sin(a3) g; for ~ z . . “ [+9143 . if Hme :— 2 W cmx :[Hfimjrw 0(X /_ (ax 00‘ (99x /? COD": (0) X (Lam )«LUU [BL/m6an ,Lw’u 1+ 9W , 2 (Wm X/L :— w Hoylwrm x—H) c ,fi (033% \ (b) d ._f for ____ esin(2t) (H (Pix 341/ w a my} :7( W kg) '2’“ e Z (méfié) ’ 07? (c) W, W 4 Question 3 (20 points) Suppose a player throws a ball into the air at time t = 0. The distance of the ball from the ground follows the function 3(t) :2 6t — t2 where t is time in seconds and s is in meters. (a) How high does the ball fly? We %M7VL4/7fij #éo {gay /: 2/le flte ch/oa‘im 2') 234a. A 0/ , - ; a :0 =9 é~ 3 560 3(3): 6% 32 = ‘? => 77w 6a” 455% ‘fmflfifm (b) When does the ball hit the ground again? We 54 I“) gawaw ’Z/zJéut Y/ z: 0 i, «:9 0/444 25 2 r 0 :3 f (5.5) a a p :59 3 0 M ’5 (5/ :5 m 44/ [fa/3 #2, 7mm (at gmmgh (c) What is the velocity and acceleration when the ball is 5m high? 55—655 =5 f2»6’{+5:0 :9(‘é'“l][ié’5j;0 “’9 m I) 53%) Saw igl/ICC- ZSJCC' M") r: *2; W, s) vfl): 6‘?“ 4/!)54/fjfi“’z fir} Ms)“ 5 Question 4 ( 20 points ) Find the slope of the tangent line to the ellipse given by .172 + 43/2 2: 4 at the point ~1/\/§). l t‘ We; m ><2+ 6‘3 2: f A}? at); mme '/c.? x l gaff/x5 1/52 (7/0 =5 2X + 83 a. o .3) {MK m 234 “a; Q {- ’ 2g- (z/K We "mt (iff- yd; A239 I'M/{44% (m. Ma (tart/6 £21462, x211” 437m:ka “(fijlw/‘élz = 3+ '3 = Zr. n05 Alla/0c g./ 71:41:21, ml We?“ 7‘" MET—MEL Wt: ,lwm/ 7‘10 é’t/a/gAa7lo 5g? a/f x: r’Wy/ 46:»y7g.‘ zQ/ z 25/ +1; “fray; 0/ '3 r! ”’ x g (ll) ’l/T—vzz) A, 72 fl 6 Question 5 (20 points) (a) By differentiating 1'2 —— y2 = 1 implicitly, show that dy/dm = m/y. (b) Then derive an expression for de/de in terms of only 3/. pk g/ fl/z gym”! ,f’. ’— ’ X 92? ('5‘); 1301112 g; 73 (5/6“?! £3331 ti ( / 01x w (7 Jihzig X5“ Cigar / ...
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This note was uploaded on 02/21/2010 for the course MAT21A 40175 taught by Professor Milton during the Fall '09 term at UC Davis.

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Midterm 2 Solution - Q1 (20 pts) Last Initial Q2 (20 pts)_...

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