Chapter 10, Problem 3RE

(a)

To determine

To plot: The curve $x=e^t,y=3e^{-2t};-\infty <t<\infty$ with its positive orientation.

(b)

To determine

To obtain: The equation in x and y for the curve $x=e^t,y=3e^{-2t};-\infty <t<\infty$ by eliminating the parameter.

(c)

To determine

To identify: The curve described by the $x=e^t,y=3e^{-2t};-\infty <t<\infty$.

(d)

To determine

To evaluate: The value of $\frac{dy}{dx}$ for the curve $x=e^t,y=3e^{-2t};-\infty <t<\infty$ at point $\left(1,3\right)$.