140Bquiz9c - dt y + sec 2 x dx dt . ii) d dt ( sin y-x ) =...

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1 MATH 140B QUIZ#9 Version A Date: Nov 2, 2007 Print Name: Instructor: Dr. Fabbri Duration: 15 minutes [ 2 ] 1. Suppose a rectanglar box with a square base has no top and a volume of 20 cubic feet. Let x denote the length of the base, and y the height of the box. In addition, let S and V denote the surface area and volume of the box respectively. Which of the following 3 statements are correct? i) x 2 y = 20 ii) S = 2 x 2 + 4 xy. iii) S ( x ) = x 2 + 80 /x. A) i) only B) iii) only C) i) and iii) only D) ii) and iii) only E) None of the 3 statements are true. [ 2 ] 2. Use implicit di±erentiation to compute y ( π, 1) where cos( xy ) + y 3 = cos( x - π/ 2) . A) - 1 / 3 B) 1/3 C) 3 D) π E) None of the above.
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2 [ 2 ] 3. Suppose that x and y are functions of t. Which of the following 2 derivatives are correct? i) d dt ( xy + tan x ) = x · dy dt + dx
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Unformatted text preview: dt y + sec 2 x dx dt . ii) d dt ( sin y-x ) = 1 2 sin y cos y dy dt-1 . A) i) only B) ii) only C) both statements are correct D) neither statement is correct [ 2 ] 4. Find the equation of the tangent line to the curve dened by x 2 y + 2 y = x 3-1 at P (1 , 0) . A) y = x B) y =-x C) y = x + 1 D) y = 2 x-1 E) None of the above. [ 2 ] 5. An expanding cell is in the shape of a sphere of radius r, and volume V = 4 3 r 3 . If the radius is increasing at 1 mm/hour then nd the rate at which the volume is increasing (in mm 3 /hour) when the radius is 10 mm. A) 400 2 B) 40 C) 400 3 D) 400 E) None of the above....
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140Bquiz9c - dt y + sec 2 x dx dt . ii) d dt ( sin y-x ) =...

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