01
Parametric curves: Points with given slope
Where on the image of
does the tangent line have slope ?
02
Parametric concavity
Find
at for the curve given parametrically by , .
03
Parametric concavity
Find the interval(s) of
on which the parametric curve is concave up.
04
Parametric arclength
Find the arclength of the curve given parametrically by
, over the time interval .
05
Minimum speed of a particle
Suppose a travelling particle has position modelled by the parametric curve:
What is the slowest speed of the particle?
06
Cycloid - Arclength and surface area of revolution
Consider the cycloid given parametrically by
. (a) Find the length of one arch of the cycloid.
(b) Suppose one arch of the cycloid is revolved around the
-axis. Find the area of this surface of revolution.