Stepwise problems - Thu. 11:59pm
Parametric curves
01
Convert parametric curve to function graph
Write the following curves as the graphs of a function
. (Find for each case.) (a)
, and (b)
, and Sketch each curve.
Calculus with parametric curves
02
Parametric curves: Points with given slope
Where on the image of
does the tangent line have slope ?
03
Parametric concavity
Find
at for the curve given parametrically by , .
Regular problems - Sat. 11:59pm
Parametric curves
04
Convert parametric curve to function graph
Write the following curves as the graphs of a function
. (Find for each case.) (a)
, and (b)
, and Sketch each curve.
05
Convert function graph to parametric curve
Find parametric curves
whose images are the following graphs: (a)
and (b)
and
Calculus with parametric curves
06
Parametric concavity
Find the intervals of
on which the parametric curve is concave up.
07
Parametric arclength
Find the arclength of the curve given parametrically by
, over the time interval .
08
Minimum speed of a particle
Suppose a travelling particle has position modelled by the parametric curve:
What is the slowest speed of the particle?
09
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.