A curve is given by the parametrisation x=e^ 3t

MATHEMATICS · Subjective · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

A curve is given by the parametrisation

x=e^{3t},\qquad y=e^{2t}+t.

(i) Determine

\dfrac{dy}{dx}

in terms of

t

. (ii) Find the slope of the tangent when

t=0

. (iii) Write the equations of the tangent and the normal to the curve at

t=0