For a plane curve defined parametrically by and

MATHEMATICS · Single correct · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

For a plane curve defined parametrically by

x=f(t)

and

y=g(t)

, which differential expression represents an infinitesimal element of arc length

ds

in terms of

t

? (a)

ds = \left(\dfrac{dx}{dt}+\dfrac{dy}{dt}\right)dt

(b)

ds = \sqrt{\left(\dfrac{dx}{dt}\right)^{2}+\left(\dfrac{dy}{dt}\right)^{2}}\,dt

(c)

ds = \sqrt{1+\left(\dfrac{dy}{dx}\right)^{2}}\,dx

(d)

ds = \sqrt{\dfrac{dx}{dt}+\dfrac{dy}{dt}}\,dt