Mathematics

Mathematics

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. a. (i) Find

\dfrac{dy}{dx}

in terms of

t

. b. (ii) Express

\dfrac{dy}{dx}

solely in terms of

x

by eliminating the parameter

t

. c. (iii) Compute

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

at the point corresponding to

t=0

.

Browse the problem library