Answers: Mathematical Preliminaries

Final results only. Come to class to ask how.

• 2.427(a) \(24\,\uv\imath - 5\,\uv\jmath\); (b) \(\sqrt{85}\); (c) not defined (you can't cross a vector with a scalar); (d) \(-29\)← Problem
• 2.429\(a = \pm 2\)← Problem
• 2.443\(x^2 - 2x + y^2 + z^2 = 1\), a sphere← Problem
• 2.445\(331\,\mathrm{N}\) and \(244\,\mathrm{N}\)← Problem
• 3.373\(f'(x) = 9x^2 + \dfrac{8}{x^3}\)← Problem
• 3.375\(f'(x) = e^{\sin x}\cos x\)← Problem
• 3.377\(f'(x) = x\sec^2(x) + 2x\cos(x) + \tan(x) - x^2\sin(x)\)← Problem
• 3.381\(y' = \cos x\,(\ln x + 1) - x\ln(x)\sin x\)← Problem
• 5.447\(-\dfrac{4}{3}\)← Problem
• 5.449\(1\)← Problem
• 5.451\(-\dfrac{1}{2(x+4)^2} + C\)← Problem