AP Calculus 25 Week Review Questions Name _________________________________
1)
3  x  2x 2
is
x 
4x2  9
lim
(A) -
1
2
(B)
1
2
(C)
1
(D) 3
(E) nonexistent

2
2)
 cos
2
x sin x dx =
0
(A) -1
3)
(C) 0
(D)
1
3
(E) 1
(B) 0
(C) 3
(D) 6
(E) none of these
The equation of the tangent to the curve y  e x ln x , where x = 1, is
(A)
(B)
(C)
(D)
(E)
5)
1
3
The maximum value on the function f x   x 4  4 x 3  6 on the closed interval
[1, 4] is
(A) 1
4)
(B) 
y  ex
y  ex 1
y  ex  1
y  ex  1
y  x 1
If the displacement from the origin of a particle moving along the x-axis is given
4
by s  3  t  2 , then the number of times the particle reverses directions is
(A) 0
(B) 1
(C) 2
(D) 3
(E) none of these
0
6)
e
x
dx equals
1
(A) 1 e
7)
9)
1
4
(B)
(C) e  1
(D) 1
1
e
(E) e  1
1
4 x  1
2
(C)
4
4 x  1
2
(D)
 16
4 x  1
2
(E)
1
16 4 x  1
2
If the position of a particle on a line at time t is given by s  t 3  3t , then the
speed of the particle is decreasing when
(A)
-1 < t < 1
(B) -1 < t < 0
(D)
t>0
(E) t  1
(C) t < 0
The curve 2 x 2 y  y 2  2 x  13 passes through (3, 1). Use the local linearization
of the curve to find the approximate value of y at x = 2.8.
(A) 0.5
10)
1 e
e
d2y
If y  ln4 x  1, then
is
dx 2
(A)
8)
(B)
(B) 0.9
(C) 0.95
(D) 1.1
(E) 1.4
11)
12)
Suppose f x   x 2 x  1 . Then f x  x3 x  2 . Over which interval(s) is the
graph of f both increasing and concave up?
I.
x0
(A) I only
13)
II.
0x
(B) II only
2
3
III.
(C) II and IV
2
 x 1
3
(D) I and IV
IV.
x 1
(E) IV only
Which of the following statements is true about the graph of f x  in question 15?
a.
b.
c.
d.
e.
The graph has no relative extrema.
The graph has one relative extremum and one inflection point.
The graph has two relative extrema and one inflection point.
The graph has two relative extrema and two inflection points.
None of the preceeding statements is true.
14)
If f x  is continuous at the point where x= a, which of the following statements
may be false?
(A) lim f  x  exists
(B) lim f  x   f a 
(D)
15)
(C)
xa
x a
f a  is defined
f a exists
(E) lim f  x   lim f a 
x a
x a
If f u   tan 1 u 2 and g u   e u , then the derivative of f g u  is
2ue u
(A)
1 u 4
2
2ue u
(B)
1 u 4
(C)
2e u
2e 2u
(D)
1  4e 2 u
1  e 4u
(E)
2e 2u
1  e 4u
Calculator Allowed
16)
Find the area bounded by y  tan x and x  y  2 , and above the x-axis on the
interval [0,2].
(A) 0.919
17)
(B) 0.923
(C) 1.013
(D) 1.077
(E) 1.494
An object in motion along a line has acceleration a t   t 
2
and is at rest
1 t 2
when t = 1. Its average velocity from t = 0 to t = 2 is
(A) 0.362
(B) 0.274
(C) 3.504
20)
x
1
f
2
2
3
4
3
4
6
(D) 7.008
f
1
2
1
2
4
(E) 8.497
g
-3
g
5
0
2
3
4
3
1
2
If K x   g 1 x  , then K 3 
(A) 
1
2
(B)

1
3
(C)
1
3
(D)
1
2
(E)
2
21)
22)
24)
25) Suppose the function f is continuous on 1  x  2 , that f x  exists on 1 < x < 2, that
f 1 = 3, and that f 2  0 . Which of the following statements is not necessarily true?
(A) The Mean-Value Theorem applies to f on 1  x  2 .
2
 f x  dx .
(B)
1
(C) There exists a number c in the closed interval [1, 2] such that f c  0.
(D) If k is any number between 0 and 3, there is a number c between 1 and 2 such
that f c  k .
(E) If c is any number such that 1 < c < 2, then lim f  x  exists.
x c
26)
dx
 x ln x equals
(A) lnln x  C
1
(B)  2  C
ln x
(D) ln x  C
(E) none of these
(C)
ln x 2
2
C
7
27)
 sin x d x 
0
(A) -2
28)
lim
h 0

(B)
2

(C) 0
(D)
1

(E)
tan / 4  h   1

h
(A) 0
(B)
1
2
(C) 1
(D) 2
(E) 
2

29)


x4 3
if x  5, and let f be continuous at x  5.
 f x  
Let 
 Then c =
x5
 f 5  c



(A) 
30)
1
6
(B) 0
(C)
1
6
(D) 1
(E) 6