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**

**Example text**

The second part we know from Ex. 6. But Tiz + r03 = 2a 3 cos 0 csc3 a (4 cos2 0 — 3 cos2 a), rot /— 27ra3 r 3 z L ( i + r0 )VE dB = — (3 sin2 a + cos2 a), J° 3 3 sin a cos a pr _ — . ira J3 g | n 2 a — 6 s i n a cos a + cos2 a — 2a(3 — 2 cos2 a)]. 3 sin a cos a Section 4 43 V is the volume common to x2 + y2 < 4a2 and (x — a)2 + z2 < a2, 22. that is, z2 < 2ax — x2. Cut into rectangular slabs perpendicular to the x-axis: 7 = 4/ [2a ( V 4 a 2 - x2) ( V 2 a x - x2) dx = 4 f a (2a - x) Vx(2a + x) dx = [ A £ A / 2 - 6 ln(3 + Vs)]as 24.

When a = d and 6c = 0 20. 4 and A' have the same characteristic polynomials. 22. 2 0 -1 1 V6 24. 2 1 -3 -1 -V6 26. 3 1 1 0 = 0, Sample Test V "l . 2, 2, a 0 ; -l, a 0 32. 0, a 2 i-i 30. 3, a 11 0 ro 29 1 V ; 3, a 0 + b 1 0 lj 34. (Ay')-x' = xAy' = yAx' = y(Xx') = Xyx' = Xy'-x' = 0 36. - | A | = | - A | = |0 - A\ = (0 - X)(0 - M) (0 - v) = -XMv. l 38. 6, A = PDP~ , where D has X, /x, J/ on the diagonal and 0 elsewhere. Clearly A = 0 if and only if D = 0. 40. Suppose Ax' = Xx', with x' ^ 0. Then A 2 x' = A (Ax') = A(Xx') = X(Ax') = X(Xx') = XV.

Set /<(x) = (df/dZi) (x). Then £ a\-/t-(x) = n/(x). Substitute fcc for EteFebruary 2018