A Second Course in Calculus by Harley Flanders PDF

By Harley Flanders

ISBN-10: 148323102X

ISBN-13: 9781483231020

Moment direction in Calculus

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Then xn > (x, y, z). Section 3, page 208 2. (x, y) product. ►/(#) and (x, y) 4. (x, y, z) > x2 + y2 + z2 continuous functions. > g(y) are continuous; so is their ► (x2 + y2 + z2)112, SL composite 6. Let x = (x,y), u = (w, v) and suppose |x — u| < e. Then \x — u\ < e and \y — v\ < e, hence l/(x) ~ / ( u ) | = 1 x+ y (u - x) + 0 - y) (x + y)(u + v) u + v \x - u\ + |y - y| 2-2 2e 4 € * (x,y). By continuity, f(z,y) = 8. Let f(xn, yn) = c and (xn, yn) lim/(x n , yn) = c, so (x, 2/) is in the set. 10.

47raw+3/(n + 3) 14. 7r/36 18. 2 16. 12. 7ra4/16 2w — 4 square units 2 27r i4a . Slice into washers by planes z — constant. Note that 2/i + 2/o = 2A. 20. Use cylindrical coordinates. Take the cone along the z-axis, apex at 0. Take the axis of the cylinder at x = a csc a, y = 0. The solid cone is de­ scribed by — rVE

More elementary: the solid is what remains after 4 tetrahedra of volume £ are cut off the cube. 29. I t is a regular octahedron of volume £. ) Section 2, page 426 2. {2, 3TT/2, - 2 } , {5V2, 7TT/4, 0}, {2, 4TT/3, -1} 4. (aW + c 8 ) 1 " 6. In matrix notation, it is merely the formulas du = wd0, dw = — u d0, dk = 0. The third is obvious. The first two are true because u and w depend only on 0, and ud = w, vt9 = — u. 8. V = / / / rdrdSdz over 0 < r < a, 0 < 0 < 2TT, 0 < 2, r/o + z/h < 1. Hence y 5 T2T V [a / fhil-r/a) -/„U(i.

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A Second Course in Calculus by Harley Flanders


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