1. Find the scalar and vector projection of b onto a. a=
a.
2.
,
b.
,
c.
,
d.
,
e.
b=
,
Find the distance from the point (0,4) to the line x+y=-2
a.
b.
c. 2
d. -5
e. 1
3. Which vector is parallel to the line 2x-5y=2
a.
b.
c.
d.
e.
4. Describe the motion of a particle with position r(t) as t varies in the given interval
>
a. Circle centered at (2,3) going clockwise
b. Ellipse centered at (0,0) going clockwise
c. Ellipse centered at (0,0) going counterclockwise
d. Circle centered at (2,3) going counterclockwise
e. Hyperbola centered at (0,0)
5.
a. ∞
b.
c.
d.
e.
DNE
-∞
6
-6
6. f and g are continuous functions and
a. 9
b. 11
c. 19
d. 7
e. 4
=4. f(2)=3. Find g(2).
7. Find an interval in which there is a solution to the equation
a. (-1, )
b. (0,1)
c. (1, )
d. (
e. (
)
8.
a.
b. 0
c.
d. 1
e. DNE
9. Find the horizontal and vertical asymptotes of the following curve.
a.
b.
c.
d.
e.
y=1, x=1
y=1, x=1, x=-1
x=1, y=1, y=-1
x=1
y=1
10. Find the constant c that makes g continuous on (
g(x)=
a. There is no such c
, )
b.
c.
d.
e.
0
2
-2
1
11. Find the derivative of the following functions
a.
b.
)
12. Find a vector equation, parametric equation, and Cartesian equation for the line that
passes through the points (-3,4) and (2,8)
13.
14. The piecewise function f is defined as follows.
(a) [5 points] Where is f discontinuous? Justify your answer.
(b) [5 points] Is f differentiable at x = 2? If so, give the value of f 0(2) and write down the
details of its computation. If not, explain why the derivative does not exist at x = 2. In
either case, justify your answer.
15. Find the points at which f(x) is discontinuous. At which points is f continuous from the
right, from the left, or neither. note: The top function should have 'if x<=-1'.
16. Using the definition of the derivative, find the equation of the tangent line to f(x)=
at the point (1,
)
17. If an arrow is shot upward on the moon with a velocity of 58 m/s, its height (in meters)
after t seconds is given by
a. Find the velocity of the arrow after 1 second
b. Find the average velocity on the time interval (1, 2)
18. Find an equation of the line tangent to
at the point (0,0)
19. Determine whether or not the derivative of f(x) exists at x=0
20. Compute the derivative of
and state the domain.