MATH 126 Midterm: MATH 126 UW Midterm 2 Winter 10bekyelExIIans

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turquoisegnu128

31 Jan 2019

School

Department

Mathematics

Course

MATH 126

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All

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Document Summary

0 q(3 cos t)2 + 12 + ( 3 sin t)2 dt == z /3. 3 (b) find the curvature at the point (cid:16) 3 3. = |h3 cos t, 1, 3 sin ti h 3 sin t, 0, 3 cos ti| = |h 3 cos t, 9, 3 sin ti| 10: evaluate the following integrals. (a) (b) Here it is easier to use polar coordinates: over the region r between the lines y = x, y = 3x and the curve y = 9 x2. 243(cid:0) 3 2(cid:1) (r cos )r3 rdrd = r6. Z 4 y/4 y ln(cid:0)x3 + 1(cid:1) dxdy. In this problem we have to change the order of integration. The region is inside the triangle with vertices (0, 0), (1, 0) and (1, 4). 0 y ln(cid:0)x3 + 1(cid:1) dydx = z 1. 3 (cid:2)(cid:0)x3 + 1(cid:1) ln(cid:0)x3 + 1(cid:1) (cid:0)x3 + 1(cid:1)(cid:3)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12)

Related Questions

1. Use Lagrange multipliers to find the least distance between the point P(?3, 0, 4) and the surface of the cone z 2 = x 2 + y 2 .

2. Evaluate ? 2 0 ? 4 y 2 y sin(x 2 )dxdy.

3. Show that the volume V of the solid in the first octant bounded by the surface z = e y?x , the plane x + y = 1, and the coordinate planes satisfy V < cosh(1)

4. Set up the integral in spherical coordinates ? 1 0 ? ? 1?x2 0 ? ? 2?x2?y 2 ? x2+y 2 xydzdydx

5. Set up in polar coordinates the following double integral ? ? R ? x 2 + y 2dA; (R) bounded by x 2 + y 2 = 2x, y ? x, y ? 0.

6. Suppose a particle moving in space has velocity v(t) = ?sin(2t), cos(t), e?t ? and initial position x(0) = ?2, 1, 0?. Find the position vector function x(t).

7. : Find the maximum value of y x over (x ? 2)2 + y 2 .

Please solve only number 4 showing work.