Expanding, splitting fractions and boundary conditions Problem set B Answers

1. (a) \(\frac{3}{4}x^{4} - \frac{5}{3}x^{3}+c\)
2. (b) \(\frac{1}{3}x^{3} - 2x^{2} - 12x+c\)

1. (a) \(\frac{4}{3}x^{3} - 4x - x^{-1}+c\)
2. (b) \(\frac{1}{5}x^{5} - 6x - 3x^{-3}+c\)

1. (a) \(3x^{3} - 4x+c\)
2. (b) \(-\frac{5}{4}x^{-2} + x^{-3}+c\)

\(-\frac{7}{3}t^{-1} - t^{-4}+c\)

1. (a) \(y=2x^{3} - 5x - 3\)
2. (b) \(y=12x + 9x^{-2} - 33\)

\(y=2x^{2} - 4x^{-2} + 2\)

1. (a) \(V=\frac{4}{3}t^{3} - 3t^{2} + 7t\)
2. (b) 30 litres

1. (a) \(y=x^{3} + 8x^{-2} + 20\)
2. (b) 29 m

\(y=\frac{1}{3}x^{3} + \frac{3}{2}x^{2} - 4x - \frac{11}{2}\)

\(y=-9x^{-1} - 2x^{-3} + 12\)