5.2 曲線

1.

(a) $${ {\bf r}(t) = (e,e^{-1},0) + t(e,-e^{-1},-1)}$$(b) $${{\bf r}(t) = (1,0,2) + t(0,\pi,1)}$$

2.

(a) $${y = \frac{b}{a^2}x^2}$$(b) $${y = x^{2/3}}$$(c) $${z = \frac{1}{2}\tan^{-1}{(\frac{y}{x})}, x^2 + y^2 = 1}$$

3.

(a) $${\log{(\sqrt{2})}}$$(b) $${\sqrt{2}(e^{\pi} - 1)}$$(c) $3$

4.

(a) $${\frac{e^{-t}}{[1+e^{-2t}]^{3/2}}}$$(b) $\cos{t}$(c) $${\frac{1}{3}}$$