By Harley Flanders

ISBN-10: 148323102X

ISBN-13: 9781483231020

Moment direction in Calculus

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**Extra resources for A Second Course in Calculus**

**Sample text**

Set s = |x|, t = |y|. Then |e"ixi2 - e-i y ' 2 | < I |x| - |y| I < |x - y|, etc. of 20 Chapter 6 20. The composite of continuous functions (x,x) >f(x9x). is continuous: x > Section 4, page 212 16. the straight line x = (3, t, 9t) 18. The graph has no interior points since each line parallel to the 2-axis intersects the graph in at most one point. Section 5, page 216 4. 2 2. 3, 4 2xy, x 8. — y2 sin x, 2y cos x 2xy + y2, x2 + 2xy 6. 10. cos x, sin y 12. - 2 sin(2x + y), -sin(2o; + y) 16. -l/(x 20.

4. Chapter 11 Locate the centroid of the plane region bounded by the curve y = sin x and the interval [0,7r] on the z-axis. Compute the volume of the solid bounded above by the surface z = 1 + x2 + y2 and below by the triangle with vertices (0, 0, 0), (2, 0, 0 ) , (0,1,0). Express / (f f(x, V) dyj dx as a sum of integrals iterated in the opposite order. 5. Compute / / ex2+^ dx dy over any quarter circle of radius 3 and center (0, 0), and show that the value of the integral does not depend on which quarter circle you choose.

It is the tangent plane to the surface f(x, y, z) = /(a, 6, c) at (a, 6, c). 18. 3. 44)(8 X 10"6)1'2 < f X 91'2 X 10"3 = (15/2) X 10- 3 < 10"2. For a better estimate, use | s i n 0 ± c o s 0 | < \/2 (instead of 2). Then M3 < ( 2 \ / 2 ) ( l . 44 X 10-3 < 5 X IO-3. Section 4, page 344 2. 12. 13. A = C = neither Pick Pick fxx(0, fw(0, 4. the the 0), 0), min 6. min 8. max 10. neither curve x = t, y = 0: g(0) = fxx(0, 0) > 0, etc. curve x = [B/(A2 + B2)l'2]t, y = [-A/(A2 + B2)v% where 2 2 B = fxy(Qy 0).

### A Second Course in Calculus by Harley Flanders

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