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Unformatted text preview: Sample Problems for the final exam MAT 21B 1)(True/False) Label the following statements as either true or false. (No explanation required. Each correct label is worth two points.) a: The circumference of a circle of radius 3 is 6. b: If a system behaves as if its entire mass was at a single point, then we call this point the center of mass. c: eln(xy) = elnx  elny d: e: 2sin2 x = 1  cos2x f: ln(2  3) = ln2  ln3 g: e7 = (e3 )4 h: If f (t) is continuous, then i: (secx + tanx)2 dx =
b a b a f (x)g(x)dx = ( b a f (x)dx)( b a g(x)dx) f (t)dt exists. (secx + tanx)3 +C 3 j: The polar coordinates of a point are uniquely determined. cosz dz, 4+3sinz 2) (8 points) Find the area bounded by the curves y = xaxis, x =  and x = . 2 2 the 3) (9 points) A conical tank of depth 10 feet and top diameter 10 feet is full of oil. Set up an integral that calculates how much work it would take to pump all the oil to the top of the tank. Oil weighs 57lb/ft3 .
1 4) (9 Points) Find the length of the curve parametrized by x = cost, y = t + sint, 0 t .
z+1 dz z 2 (z1) 5) (9 points) (Section 8.2  8.5) Find 6) (9 points) (Section 8.2  8.5) Find 2 dx, x x3 x2 1 >1 7) (9 points) (Section 8.2  8.5) Find 2 0 sin7 xdx 8) (9 points) (Section 8.2  8.5) Find
1 0 x3 ex dx 9) (9 points) Find the integral xlnxdx, if it exists. 10) (9 points) Sketch the curve given by the polar equation r = sin2. 2 ...
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This note was uploaded on 04/16/2008 for the course MATH 21B taught by Professor Vershynin during the Spring '08 term at UC Davis.
 Spring '08
 Vershynin
 Math

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