Read e-book online A Second Course in Calculus PDF

By Harley Flanders

ISBN-10: 148323102X

ISBN-13: 9781483231020

Moment direction in Calculus

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Extra info for A Second Course in Calculus

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2tww; inverse: 1/ = (yz/x)m} v = (zx/y)112, w = (xy/z)112 on the domain x>0,y>0,z>0. 8. x > x/p 2 where p2 = z2 + 2/2 + z2. The Jacobian is — 1/p6. Section 6, page 501 2. 4. F = arc cot $ - \t l n ( l + *2) + t In Z, F ' = - | l n ( l + t2) + In * F = (1 + *)-i, F ' = - (1 + t)~2 6. ra2 10. / (/ 8.

The right triangle of base a revolves about its leg of length h into a right circular cone, x = ^a, A = £a/i, and V = ^wa2h = 27rx4. 14. A = area of sphere = 47ra2, L = length of semi-circle = xa, = 2a/7r. 16. (0, 0, f (2a - A) 2 /(3a - h)) x = A/2TL 17. The total force due to gravity is /// f 5(x) dV = Mi. The total torque due to gravity is /// x X f «(x) dV = ( j y y x «(x) dV) X f = MX X f = x X ( M ) . 18. x = £(a + b + c). To see this, take a triangle with base on the x-axis and height h measured on the 2/-axis.

Section 8, page 367 2. equilateral 4. cube 6. 8. If xyz 5* 0, then by Ex. 7, cube c * ) ( > ) ( * ) < i.. \x + y + z) \x + y + z) \x + y + z) 10. q If x > 0, y > 0, or z > 0, apply Ex. 9 to x/(x 27 9 + y + zq)1,q, etc. 12. f, at (£, -£, — -£). 14. 272. [Suppose x = y. Then z2z = 1 and 2x2 + z2 = \7-, hence 423 — 17z + 8 = 0, that is, tz — 17t + 16 = 0, where Z = 2z. By inspection, 2 = 1 is a root, so t2 - 17* + 16 = (t - 1) (t2 + t - 16). ] 16. / ( * , 2/, 0) = a? + y2 > 0 = /(0, 0, 0). SAMPLE TEST 1.

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A Second Course in Calculus by Harley Flanders


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