Midterm1v2Solution - Name (Please print) Section Midterm 1...

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Unformatted text preview: Name (Please print) Section Midterm 1 February 1, 2011 1. Find the volume of a solid by slicing it perpendicular to y-axis. The base of Jo the solid is the disk £132 + y2 g l. The cross sections by planes perpendicular to the y—aXis between y = —1 and y = 1 are isosceles right triangles with one ' Ssfl'wfim: m a.” 4% 4i J/g/=!/J—?%@ 714 m 4mg;ny 49) = f sari/475).?) W” M“ Viz/5”! =fz/4M= vet—ff = — —4 :2-1{5+1-g=% W 2. Find the length of the curve given by the formula x = y; + Ely— from y = 1 to y = 3. (Hint 1 + (dx/dy)2 is a perfect square). 3 GE 3 3 3 ” 3 3 = / A; - l My J; =1W¢=Mg9§= 3. The graph of y = I2 on 0 3 LL” 3 2 is revolved about the y—aXis to form a tank Q10 that is filled with salt water (weighing 100 lbs/ft3). How much work does it take to pump all of the water to the top of the tank? I ,, . *5/qu dfafihyaaddra/Ja/Aaww j 15‘s 0M 5’0 W‘lt’ali AW: 7(wa‘g'f,(q_g) 2 q “'th f=ltoa 45/135qu 9:! .— War ': 1- _ _ 1 MW lllglfll’lll‘ 5W“)? filler—Mm (la‘%)2 :93) z 0 ~ 'rr _ = 91;}: (32—625)=qrf (32-11%): log-- 190$!- = 3%,!le— : 4. Let = $3 — 3.732 — l, I Z 2. Find the value of df‘l/dx at the point (IS FE) 1’ = —1 = 13(3). ; _l w W W W +§wa¥°rm ii = $2 6am?) [fie =—1. my all; maflal (dz)l.c:ou id = f=t3flg7= 33/2563 = $9 ( ‘ "z' xx=3 I 4. J. 5. Use logarithmic differentiation to find the derivative of y, Where y = (ISfls) _ WW! I g = :22 (m—ajLsz-H) 1(r—2) 12—4—1 g 3 6.Eva,lua,,e ,heine m: W. t; mm @ ' j: 465 :‘au'effl- J“ — é l-f/ — l+e* +S4orwbs_ /+u _ a +6 — —_ 64 [He‘L/Jc (L = 5» (Mafia "Lg 70” “My (10 FE) 7. (Extra credit) Solve the initial value problem: £4: 61—31, y(0) : 0 go; 67"}: x0!“ 0: flLée’w) y x 0: &(I+C) $5Q=S€¢ e'= I+c K 4— ...
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Midterm1v2Solution - Name (Please print) Section Midterm 1...

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