# idea - 3 y-2 z = 12 take y = z = 0 one can get x = 12 that...

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Solutions to Test II Problem 1 Z xln (3 x ) dx = x 2 2 ln (3 x ) - Z x 2 2 1 x dx = x 2 2 ln (3 x ) - Z x 2 dx = x 2 2 ln (3 x ) - x 2 4 + C Problem 2 Part(a) Average = 1 4 - 0 Z 4 0 xdx = 4 3 Part(b) Volume inside = π Z 16 0 ( x ) 2 dx = 128 π Volume cylinder = π × 4 2 × 16 = 256 π Hence Volume solid = 256 π - 128 π = 128 π Problem 3 For present value, since we are given money ﬂow rate f ( t ) = 10000 + 400 t , interest rate r = 0 . 2 and time t = 20, we can set up the integral: P = Z 20 0 (10000 + 400 t ) e - 0 . 2 t dt . Evaluate the integral with integration by parts, one can get P = (10000 + 400 t ) e - 0 . 2 t - 0 . 2 | 20 0 - Z 20 0 400 e - 0 . 2 t - 0 . 2 dt = (10000 + 400 t ) e - 0 . 2 t - 0 . 2 | 20 0 - 400 e - 0 . 2 t ( - 0 . 2)( - 0 . 2) | 20 0 = 58168 . 436 . 1

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Problem 5 Part(a) For the plane x +
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Unformatted text preview: 3 y-2 z = 12, take y = z = 0, one can get x = 12, that is, (12 , , 0) is the x intercept. Similarly, (0 , 4 , 0) is the y intercept and (0 , ,-6) is the z intercept. Part(b) f ( x , y , z ) = x 2 y + e 3 xz + y 2 f x ( x , y , z ) = 2 x y + e 3 xz + y 2 3 z f y ( x , y , z ) =-x 2 y 2 + e 3 xz + y 2 2 y f x ( x , y , z ) = e 3 xz + y 2 3 x 2...
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## This note was uploaded on 05/27/2011 for the course ECON 201 taught by Professor Caltech during the Spring '10 term at Wisc Eau Claire.

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idea - 3 y-2 z = 12 take y = z = 0 one can get x = 12 that...

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