M
ATH
150: S
EMINAR
#13 Q
UESTIONS
Content:
Section 10.1:
Curves Defined by Parametric Equations
Section 10.2:
Calculus with Parametric Curves (Tangents only)
Section 10.3:
Polar Coordinates
Questions:
1. One of the graphs below is the graph of following parametric equations:
x
=
t
+ sin 4
t,
y
=
t
2
+ cos 3
t
Indicate which one. Give reasons for your choice.
*2. Find an equation to the tangent line to the curve
x
=
√
t,
y
=
t
2

2
t
at the point corresponding to
t
= 4
.
3. Find an equation of the tangent to the curve
x
= 1 +
√
t,
y
=
e
t
2
,
at the point
(2
, e
)
by two methods:
(a) Without eliminating the parameter.
(b) First eliminating the parameter.
4. Find an equation of the tangent to the curve
x
= sin
πt,
y
=
t
2
+
t
at the point
(0
,
2)
. Then graph the curve and the tangent.
*5. Let
x
=
t
2
+ 1
,
y
=
e
t

1
.
(a) Find
dy/dx
.
(b) Find
d
2
y/dx
2
.
(c) For which values of
t
is the curve concave upward?
6. Given the parametric curve
x
=
t
(
t
2

3)
,
y
= 3(
t
2

3)
.
(a) Find the
y
intercepts of the curve.
(b) Find the points on the curve where the tangent line is horizontal or vertical.
M
ATH
150: S
EMINAR
#13 Q