MATH 2110 – EXAM 2 REVIEW PROBLEMS
This is not a comprehensive set of problems. Be sure to review your notes and
homework when preparing for the exam.
1. Find the domain of r(t) =
2 2
4 , , 6
t t t
< − − >
2. Sketch the space curve for each vector equation:
a.) r(t) = <sin t, 3, cos t>
b.) r(t) = < sin t, t, cos t>
What is the difference between these curves?
3. Find the derivative of each function:
a.) r(t) =
2 2
1,cos ,
3 1
t t
t
< >
−
b.)
r
(t) =
4
4
t
e
i
– ln(6t – 5)
j
+ (sin t)
k
4. A golf ball is struck from ground level at an angle of 45°. The ball lands 10 m away.
a.) Find the ball’s initial speed
b.) For the same initial speed, find two angles of inclination that produce a range
of 6 m
5. In a shot put trial, an Olympic athlete throws a 16-lb ball at an angle of 45° to the
horizontal from 6.5 feet above the ground at an initial speed of 44 ft/sec. How long does
it take the ball to hit the ground and how far does it travel?
6. Find and sketch the domain of f(x, y) =
2 2
9
x y
x
+ −
7. Sketch the level curves for f(x, y) =
2 2
64
x y
− −
for k = 0, 2, 4, 6, 8. What is the
graph of f(x, y)? (i.e., what surface is described by f(x, y)?)
8. Evaluate:
a.)
2
2 2
2 2
( , ) (0, 0)
lim
x y
x y
x y
→
−
+
b.)
2
4 2
( , ) (0, 0)
lim
x y
x y
x y
→
−
+
