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exam 2, calc 2 - Ix and I y(a fCx,y/0 Question 4 Let[ex y =...

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Math 351 Exam 2 (8.2-9.4) Summer 2010 American River College Terry , Directions: Closed book. Closed notes. No collaboration. Answer each question on the paper provided. There is not enough room on this paper to answer questions, so it is in your best interest only to use tne paper provided by the instructor, as. illegible work can not be graded. Exam ends at 2:30pm. Question 1: Find each integral. If the integral is improper, be sure to mention whether it converges or diverges. (5 points each) 2 (a) f x e 3x dx (b) f 1 \1 - x 2 )e 2X dx (c) {X) 1 d 2 x In(x) X fX) (d) o xe- X 2 dx Question 2: (5 points) A computational biologist has determined that the rate at which a pollutant is being dumped into a small streamat time t days is given by R(t) = lOOOe- o . o6t tons per day. Find the total amount of the pollutant that will be released into the stream into the indefinite future. Question 3:
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Unformatted text preview: Ix and I y . (a) fCx,y) /0 Question 4: Let [ex, y) = 6x 2 + 6y 2 + 6xy + 36x -5. (a) (5 points) Find all critical points for f. (b) (5 points) Determine whether each critical point is a local maximum, local minimum, saddle point, or inconclusive. Question 5: Use differentials to approximate '/6.07 2 + 7.95 2 . (5 points) SX 2 +y2 Question 6: (5 points) Let W = . Evaluate dw for x= -2, y=l, z=l, dx=0.02, z+l dy= -0.03, dz=0.02. f;r 2 (; (f) (0) J '-o x + '2. . 21 o ..L Z7 I :: .l (I -L{) ,-i -/2 I "2-, 7--2. Y -\ , -:= I\ lI'lA. . b, fb &.1 --"2---,. S J~ b \ c\ lV\. \ l"l \0-l' U \~ \~ \ ClO l"2-I --'1.-) o I t#\. ,--7.-/ J .1 (. ") ~ /0 ..J { C o -( ..--C o 000 --(()-/000 / (: ;;)- ( J ( --( --(. ) ( ( , --r A ~ + (/ I ------~ . I 5 CJ -0 I ( ! I ( ) \ I , , -\I --=-= , (,-I ( ( { -( ) 2· (~ ~-----( / - ------( o. 2...
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