Answers to quiz 5

1,2. dM/M2 = dm1/m12 + dm2/m22
dM/M = M/m1·dm1/m1 + M/m2·dm2/m2
if m1 = 2m, m2 = m, then M = (2/3)m and dM/M = (1/3)dm1/m1 + (2/3)dm2/ m2
1: (1/3)2% + (2/3)(−1%) = 0 (M doesn't change)
2: (1/3)(−1%) + (2/3)2% = 1% (M increases by 1%)

3. f = sinh xy, fy = x cosh xy, fxy = cosh xy + xy sinh xy
3. g = cosh xy, gy = x sinh xy, gxy = sinh xy + xy cosh xy
ggxy − ffxy = xy

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