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MAC2313_Test2_Spring2010

# MAC2313_Test2_Spring2010 - Page 1 of4 MAC 2313 Name Test 2...

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Unformatted text preview: Page 1 of4 MAC 2313 Name Test 2 Date: February 1 l, 2010 Clearly show all work for full credit. 1. (8 points) Find r(!) if r”(t) = 2i+6tj+l2t3k and r'(0) 2i and r(0) :j—k. 2. (8 points) Find the length ofthe curve given by r(t) = 4sin(t)i — 3tj + 4cos(t)k , where 0 S t S 3 . 3. (8 points) A plastic bucket (right circular cylinder) has diameter 20 inches and height 20 inches. The plastic is 0.5 inches thick. Use differentials to estimate the amount of plastic (in cubic inches) needed to make the bucket. Page 2 of4 4. (8 points) On the same xy’plane, draw the level curves associated with K: -1, 0, l, and 2, for the function f(x,y) = w/y — .vc3 . Label one point on each curve. xy . . . ——-7 - (Jay) 7: (0,0) 5. (8 pomts) Determme whether the function f (x,y) = x + xy + y %"'(x,y) = (0,0) is continuous. Explain your reasoning. 6. (8 points) Suppose r(t) =< [,12 ,t2 >. Determine an equation ofthe normal plane at the point (1,1,1). Page 3 of4 7. (8 points) A sequence of periodic payments of 1 forms an annuity. The present value of this annuity, z, is a function of the interest rate used for discounting the payments, I, and the number of payments, N. Symbolically, .. =f( I , N). The table below shows present values for the given values of] and N. Use the table to determine a linear approximation of the present value when the interest rate is 5.75% and there are 16 payments. _-——- -10 -8.53 -7.72 _7.02 -6.42 N 20 14.88 12.46 10.59 9.13 25 17.41 14.09 11.65 9.82 8. (8 points) Determine the curvature of r(t) =< t2 ,0,t > at the point (0,0,0). 9. (8 points) Given f(x,t) : e" sin(2xt) , determine f;(1,0). Page 4 of 4 10. (8 points) Given ln(xyz) = z — x, ﬁnd 22—. Simplify answer completely. 0)” l 1. (6 points each) You are given u(x,t) = sin(x — at). (a) Determine u,,. (b) Determine un . 12. (8 points) Suppose f is a differentiable function of x and y, and g(u,v) = f(2u — v,v2 — 411). Use the table below to calculate gv(l,2). ...
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MAC2313_Test2_Spring2010 - Page 1 of4 MAC 2313 Name Test 2...

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