Math 4A – Castroconde
Name:
Worksheet 2 – Chapter 14
I.D.#:
Do your work on separate sheets of paper.
Attach this page to your work.
1.
Find
5
0
sin( )
lim 2 ,
,
t
t
t
t
e
t
→
.
2.
Find the derivative of the vector function
1
( )
,
,
t
r t
t
e
t
−
=
G
at
t
= 1.
3.
Find the tangent vector to the curve defined by the vector function
2
3
( )
,
,
r t
t t
t
=
G
at the point corresponding to
t
= 1.
4.
Find the unit tangent vector to the curve
2
:
( )
sin( ), 2 ,
C r t
t
t t
=
G
at the point
corresponding to
t
= 0.
5.
The position of a particle at time
t
is given parametrically by
3
2
3
,
3
t
t
x
y
t
−
=
=
.
Show that the particle crosses the
y
-axis three times.
6.
Evaluate
1
2
0
ˆ
ˆ
(
2
)
ti
t j dt
−
∫
7.
Let
2
( )
2 , sin( ),
cos( ) ,
( )
1,
,
u t
t
t
t
v t
t
t
=
−
=
−
G
G
.
Find
[
]
( )
( )
d
u t
v t
dt
×
G
G
.
8.
Find the points on the curve
2
3
:
( )
2 ,
12
C r t
t
t t
t
=
+
−
G
where the tangent vector is
horizontal or vertical.
9.
Consider the curve
2
2
:
( )
,
,1
C r t
t t
t
=
−
G
.
Find the unit tangent vector, the unit
normal vector, and the curvature of

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