Curve sketching)

Exercise

1.: Draw the outline of the following curve．
(a): $\displaystyle{y = \frac{1}{1 + e^{x}}}$
(b): $\displaystyle{y = \frac{1-x}{1 + x}}$
2.: Draw the outline of the following curve．
(a): $\displaystyle{r = a\cos{\theta}, \ a > 0}$ (circle)
(b): $\displaystyle{r = 3\theta}$ , spiral
(c): $\displaystyle{r^2 = 4\cos{2\theta}}$ lemniscate