A curve is represented parametrically by x=e^ 2t

MATHEMATICS · Multi-part · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

A curve is represented parametrically by

x=e^{2t}, \qquad y=e^{t}\sin t, \qquad t\in\mathbb R.

Answer the following questions. (i) Find

\dfrac{dy}{dx}

in terms of

t

. (ii) Express

\dfrac{dy}{dx}

solely in terms of

x

by eliminating the parameter

t

. (iii) Compute

\dfrac{d^{2}y}{dx^{2}}

at the point corresponding to

t=0