CalcAB2APRev1
Name
AP Calculus AB AP Review 2.1
1. If
( )
lim
xa
fx L
→
=
, where L is a real
number, which of the following must be
true? Justify your answer.
a. f'(a) exists
b. f(x) is continuous at x = a
c. f(x) is defined at x = a
d. f(a) = L
e. none of the above
2. If
2
3
4
yx
=+
, then dy/dx=
a.
( )
2
2
6
4
x
x
−
+
b.
( )
2
2
3
4
x
x+
c.
( )
2
2
6
4
x
x+
d.
( )
2
2
3
4x
−
+
e.
3
2x
3. If
( )
fx x=
, then f ’(5) =
a. 0
b. 1/5
c. 1
d. 5
e. 25/2
4. The position of a particle moving along
a straight line at any time t is given by
( )
2
44st t t=++
. What is the
acceleration of the particle when t = 4?
a. 0
b. 2
c. 4
d. 8
e. 12
5.
2
3
11dx
dx x x
−+
at x = -1 is
a. -6
b. -4
c. 0
d. 2
e. 6
6. If the position on the x-axis at time t is
2
5t−
, then the average velocity of the
particle for 0 ≤ t ≤ 3 is
a. -45
b. -30
c. -15
d. -10
e. -5
