Which trig identity
should you use to
integrate
Z
sin5 (x)dx
Section 8.4
Level: Easy
A sin2 (x) +
cos2 (x) = 1
B sin2 (x) =
1−cos(2x)
2
C cos2 (x) =
1+cos(2x)
2
For
Z
sin3 (x) cos(x)dx
Section 8.4
Level: Easy
substitute u =
A sin3 (x)
B sin(x)
C cos(x)
Which trig identity
should you use to
integrate
Z
sin4 (x)dx
Section 8.4
Level: Easy
A sin2 (x) +
cos2 (x) = 1
B sin2 (x) =
1−cos(2x)
2
C cos2 (x) =
1+cos(2x)
2
Which trig identity
should you use to
integrate
Z
sin2 (x) cos3 (x)dx
Section 8.4
Level: Easy
A sin2 (x) +
cos2 (x) = 1
B sin2 (x) =
1−cos(2x)
2
C cos2 (x) =
1+cos(2x)
2
With
sZ = sin, c = cos,
sin3 (x) cos2 (x)dx =
A
Section 8.4
Level: Hard
B
C
D
E
c5 x c3 x
−
+C
5
3
c6 x c4 x
−
+C
6
4
c4 x s3 x
−
+C
4
3
c3 x s2 x
+
+C
3
2
−c3 x · s2 x + C
Are the graphs
y = x2 and x = y 2
functions?
A Both graphs are
NOT functions
Section 7.1
Level: Easy
B x = y 2 is the
only function
C Both graphs are
functions
D y = x2 is the
only function
When does
f (x) = ax+b
cx+d have an
inverse?
A da − cb 6= 0
B ab − cd 6= 0
Section 7.1
Level: Hard
C da − b > 0
D ba − dc < 0
E We cannot
determine
without
knowing the
values.
Section 7.1
Level: Easy
If is differentiable
then f is
one-to-one.
A True
B False
What is the domain
of asin(x)
Section 7.7
Level: Easy
A [− π2 , π2 ]
B [0, π]
C [−1, 1]
Section 7.7
Level: Easy
Rewrite 4x − x2 by
completing the
square
A 4 − (x − 2)2
B 4 + (x − 2)2
C (x − 2)2 − 4
Simplify
4
sin(acos( y9 ))
A
Section 7.7
Level: Hard
B
C
D
y4
9
p
81 − y 8
9
9 − y4
9
y4
Identify
Section 7.7
Level: Easy
d
asin(x)
dx
1
1 − x2
1
B
1 + x2
1
√
C
|x| x2 − 1
A √
Identify
Section 7.7
Level: Easy
d
atan(x)
dx
1
1 − x2
1
B
1 + x2
1
√
C
|x| x2 − 1
A √
Identify
Section 7.7
Level: Easy
d
asec(x)
dx
1
1 − x2
1
B
1 + x2
1
√
C
|x| x2 − 1
A √
Section 7.7
Level: Easy
Identify
Z
1
√
dx
1 − x2
A asec(x) + C
B atan(x) + C
C asin(x) + C
Identify
Section 7.7
Level: Easy
Z
1
dx
1 + x2
A asec(x) + C
B atan(x) + C
C asin(x) + C
Section 7.7
Level: Easy
Identify
Z
1
√
dx
x x2 − 1
A asec(x) + C
B atan(x) + C
C asin(x) + C
2
5
+1)
ln( (x√1−x
)=
5 ln(x2 + 1)
A 1
2 ln(1 − x)
Section 7.2
Level: Easy
B 5 ln(x2 + 1) +
ln(1 − x)
C 5 ln(x2 ) ln(1) −
1
2 ln(1) ln(−x)
D 5 ln(x2 + 1) −
1
2 ln(1 − x)
Which interval is
x − 4 ln(x + 1)
one-to-one
Section 7.2
Level: Hard
A (0, ∞)
B (0, e − 1)
C (3, ∞)
D ( 4e − 1, ∞)
What is
Section 7.2
Level: Easy
A ex
B x0
1
C
x
d
ln(x)?
dx
What is ln(e)?
Section 7.2
Level: Easy
A 0
B 1
C e
What is
Section 7.2
Level: Easy
Z
A 1
B x0
C ln(x)
D e
1
dx?
x
Section 7.2
Level: Easy
How can we
rewrite loga (x) in
terms of ln?
ln(a)
A
ln(x)
B
ln(x)
ln(a)
C It cannot be
done
For
Section 7.2
Level: Easy
Z
tan(x)dx
substitute u =?
A sin(x)
B cos(x)
C tan(x)
The set of all points
(et , t) where t is a
real number is the
graph of y=
Section 7.3
Level: Hard
A
1
ex
1
B ex
C ex
D
1
ln(x)
E ln(x)
What is the Domain
of ex
Section 7.3
Level: Easy
A (0, ∞)
B (−∞, ∞)
C [0, 1]
Simplify eln(x
Section 7.3
Level: Easy
2
A ex
2
+1
B ln(x2 + 1)
C x2 + 1
+1)
√
e r
√ dr
For
r
substitute u =
Z
Section 7.3
Level: Easy
√
A e r
√
B
r
1
C √
r
ex + 1
dx =?
ex
under the
substitution
Z
u
A
du, u =
u−1
ex + 1
Z
−(1 +
B
Z
Section 7.3
Level: Easy
eu )du, u = −x
Z
u+1
C
du, u =
u
ex
Z
D
udu, u =
What is
Section 7.3
Level: Easy
d x
4 ?
dx
A x4x−1
1 x
B
4
ln(4)
C ln(4)4x
Which is a general
solution to
y 0 + 2y = e−x
A y(t) = 2e−x + C
Section 9.1
Level: Hard
B y(t) = Ce−x
C y(t) =
e−2x + Ce−x
D y(t) =
Ce−2x + e−x
E y(t) = e−2x +e−Cx
Which is a general
solution to
2
y 0 + y = 1+4e
2x
Section 9.1
Level: Hard
A (atan(2ex ) +
C)e−x
cos(x)
+C
x
C (asec(2ex ) +
C)e−x
B
Section 9.1
Level: Easy
Which of the
following
differential
equations is
separable?
2
A y 0 = e−t − 2yt
B xy 0 +y = − sin(x)
C y 0 = x1 (2 − y)
Section 9.1
Level: Easy
Which of the
following is a
first-order
differential
equation
A y 0 + y = ex
d2 y
=2
dt2
C y 00 + 2y = 4
B
If f 0 (x) = −f (x)
and f (1) = 1 then
f(x)=
Section 7.5
Level: Hard
A 1/2e−2x+2
B e−x−1
C e1−x
D e−x
E −ex
Section 7.5
Level: Easy
What is the solution
dy
to
= Ky
dx
A cos(Kx) + C
B CeKx
C Ky + C
If f (t) = 3000e2t/5
and f (t1 ) = 7, 500,
find f (t1 + 5)
Section 7.5
Level: Hard
A 1200e2
B 3000e2
C 7500e2
D 7500e5
E 15000/7e7
e4x
For
dx
1 + e4x
substitute u =
Z
Section 8.1
Level: Easy
A 1 + e4x
B e4x
C 1 + 4x
How do you
Z
evaluate
Section 8.1
Level: Easy
1
x2 + 4
A u-substitution
u = x2 + 4
B inverse trig
How do you
Z
evaluate
Section 8.1
Level: Easy
x
x2 + 4
A u-substitution
u = x2 + 4
B inverse trig
How do you
evaluate
Z
1
dx
x2 + 10x + 26
Section 8.1
Level: Easy
A u-substitution
u = x2 +10x+26
B Complete the
square, its
natural log
C Complete the
square, its
inverse trig
Which integral
cannot become
Z
wn dw by
Section 8.1
Level: Easy
substitution?
Z
x sin(x2 )dx
A
Z
1
B
dx
x ln(x)
Z
1
C
dx
tan(x)
Z
D
x2 (x3 + 3)dx
Which integral
cannot become
Z
wn dw by
Section 8.1
Level: Easy
substitution?
Z
4x3 + 3
√
dx
A
x4 + 3x
Z
ex − e−x
B
dx
(ex + e−x )3
Z
2x
√
C
dx
x2 + 1
Z
sin(x)
D
dx
x
For
Section 8.2
Level: Easy
Z
e2x (3x)dx by
parts u =
A e2x
B 3x
For
Section 8.2
Level: Easy
Z
x sin(x)dx by
parts v 0 =
A sin(x)dx
B xdx
For
Section 8.2
Level: Hard
Z
x2 sin(x)dx,
how many times
integrate by parts?
A 1
B 2
C 3
For
Z
asin(t)dt by
parts u =
A asin(t)
Section 8.2
Level: Easy
B 1
C You don’t use
integration by
parts for this
problem
Z
ln(t)
dt by
t
parts u =
For
Section 8.2
Level: Easy
A ln(t)
1
t
C t
B
By
Z parts
x · atan(x)dx =
Z
A − Bdx What is
B?
Section 8.2
Level: Hard
1 + x2
A
2x
2x
B
1 + x2
atan(x)x2
C
2
x2
D
1 − x2
Section 8.2
Level: Easy
Integration by parts
u = x and v 0 =(rest)
is a reasonable
choice for
Z
x(ln x)2 dx
A
Z
3
B
x2 ex dx
Z
C
x sin(x)dx
Z
x
D
dx
ln x
Which of the
following is in the
partial fraction
decomposition of
(1 + 10x)2
(x3 − x)2 (x2 − 4x + 3)
Section 8.3
Level: Easy
A (A + Bx)3
A
x
Ax + B
C
x3 − x
A
D
x−4
B
Which of the
following is in the
partial fraction
decomposition of
(1 + 10x)2
(x3 − x)2 (x2 − 4x + 3)
Section 8.3
Level: Easy
A Ax + B
A
B 3
x
Ax + B
C
(x2 − 1)2
D
A
x+4
Section 8.3
Level: Hard
What is the
remainder when
you divide
x4 + x2 + 1 by x3 + x.
A 1
B x
1
C
x
Section 8.3
Level: Easy
Which of the
following are terms
in the partial
fraction
decomposition of
x+8
x2 + 6x + 8
A
A
x−2
A
B
(x + 4)2
C
A
x+2
Which integration
technique should
be used to evaluate
Z
2 + 5x
(1 + x)2
Section 8.3
Level: Easy
A integration by
parts
B u-substitution
u=1+x
C Partial Fraction
Decomposition
D Inverse Trig
Functions
Which integration
technique should
be used to evaluate
Z
2
(1 + x2 )2
Section 8.3
Level: Easy
A integration by
parts
B u-substitution
u=1+x
C Partial Fraction
Decomposition
D Inverse Trig
Functions
Section 8.5
Level: Easy
Which of the
following integrals
yield an asin
function upon
integration after an
appropriate
substitution?
Z
x
A
dx
4 − x2
Z
4
B
dx
4 + x2
Z
x
√
C
dx
4 − x2
Z
Section 8.5
Level: Easy
To evaluate
Z
x3
√
dx which
1 − x2
trig substitution
should we make?
A x = sin(θ)
B x = tan(θ)
C x = sec(θ)
To p
evaluate
Z
1 − x2 dx which
Section 8.5
Level: Easy
trig substitution
should we make?
A x = sin(θ)
B x = tan(θ)
C x = sec(θ)
Section 8.5
Level: Easy
To evaluate
Z
2
√
dx
x3 x2 − 1
which trig
substitution should
we make?
A x = sin(θ)
B x = tan(θ)
C x = sec(θ)
Section 8.5
Level: Easy
To evaluate
Z
x+2
p
dx
(9x2 + 4)3 )
which trig
substitution should
we make?
A x = 2/3 sin(θ)
B x = 2/3 tan(θ)
C x = 2/3 sec(θ)
Section 8.5
Level: Hard
To evaluate
Z
1
√
dx
(x − 1)2 x2 − 2x
which trig
substitution should
we make?
A (x − 1) = sin(θ)
B (x − 1) = tan(θ)
C (x − 1) = sec(θ)
For
Z
√
use
Section 8.5
Level: Easy
1
dx
6x − x2 − 8
A Integration by
parts
B Partial Fractions
C Long Division
D Completing the
Square
For
use
Section 8.5
Level: Easy
Z
x2
√
dx
1 − x2
A Integration by
Parts
B Partial Fractions
C Long Division
D Completing the
square
E A trig subsitution
For
use
Z
x sin(x)dx
A Integration by
Parts
Section 8.5
Level: Easy
B Partial Fractions
C Long Division
D Completing the
square
E A trig subsitution
Z
Section 8.8
Level: Easy
1
∞
1
dx does
x2
A converge
B diverge
Z
Section 8.8
Level: Easy
1
∞
1
√ dx does
x
A converge
B diverge
Section 8.8
Level: Easy
Which are improper
integrals?
Z ∞
sin(x)
dx
A
x
1
Z 5
1
B
dx
x
4
Z 10
C
f (x)dx
−10
where
f (x) =
1
x
+ 2 −10 ≤ x ≤
−1 ≤ x ≤
1
x+2
For which functions
f(t) is lim+ f (t) = ∞
Z t→0
1
but
f (t)dt is
Section 8.8
Level: Easy
finite
0
A f (t) =
1
t
B f (t) =
1
t1/2
1
t3
C f (t) =
For which functions
f(t) is lim f (t) = 0
Z t→∞
∞
but
f (t)dt
Section 8.8
Level: Easy
1
diverges
A f (t) =
1
t2
B f (t) =
1
t1/2
1
t3
C f (t) =
Does
Z ∞ the integral
e−x dx converge
Section 8.8
Level: Easy
1
or diverge?
A converge
B diverge
Section 8.8
Level: Easy
Does
Z ∞ the integral
1
dx
ln(x)
1
converge or
diverge?
A converge
B diverge
Section 8.8
Level: Hard
Does
Z ∞ the integral
1
dx
x2 + 2
1
converge or
diverge?
A converge
B diverge
Section 8.8
Level: Hard
Does
Z ∞ the integral
2 + cos(x)
dx
x
π
converge or
diverge?
A converge
B diverge
Which of the
following functions
has smaller
growth?
Section 7.6
Level: Easy
1
x2 + x
1
B 2
x
1
C 3
x
A
Section 7.6
Level: Easy
Which of the
following functions
grows faster than ex
A x+3
B 4x
C ex /2
Section 7.6
Level: Easy
Which of the
following functions
grows faster than x2
A x+3
B x3
C ln(x3 + 2)
Section 7.6
Level: Easy
Which of the
following functions
grows at the same
1
rate as √
x2 + 1
1
A
x
1
B 2
x
1
C √
x
Section N1
Level: Easy
Which of the
following would
you compare
x3 + x2 + 1
to
x4 − x2
A x
1
B
x
1
C 4
x
Which of the
following would
you compare
2
√ to
x2 − x
Section N1
Level: Easy
1
x
1
B √
x
A
C
1
x2
Section N1
Level: Easy
Which of the
following would
ln(x)
you compare
x
to
1
A
x
1
B √
x
C
1
x2
Which of the
following would
you compare sin( x1 )
to
Section N1
Level: Hard
A cos( x1 )
1
B √
x
C
1
x
What are all the
values Zof p, for
∞
2
which
dx
xp+1
1
converges?
A p < −1
Section N1
Level: Hard
B p>0
C p>1
D p>2
E There are no
values of p for
which the
Section 11.1
Level: Easy
Identify an for the
sequence
2, 4, 6, 8, . . .
A 2n
B n+2
C 2n
Identify an for the
sequence
1
1, − 41 , 19 , − 16
,...
Section 11.1
Level: Easy
(−1)n+1
2n
1
B
(−2)n
A
(−1)n+1
C
n2
Section 11.1
Level: Hard
Identify an for the
sequence
0, 3, 8, 15, 24, ldots
A n + (2n − 1)
B n2 − 1
C 2n − 1
The statement
lim an = L means
n→∞
that for each > 0
there exists an N
such that
A If | n1 | ≤ , then
|an − L| < N
Section 11.1
Level: Easy
B If |an − L| ≤ ,
then n ≥ N
C If |an − aN | < ,
then L < n
D If n ≥ N , then
Which of the
following
sequences has this
graph
Section111.eps
Section 11.1
Level: Easy
8
n+1
8n
B
n+1
A
C 4(.5)n−1
4n
D
n!
Section 11.1
Level: Easy
Identify the value of
1 − 2n
the lim
n→∞ 1 + 2n
A -1
B 0
C 1
D ∞
Section 11.1
Level: Easy
Identify the value of
sin n
the lim
n→∞ n
A 1
B 0
C DNE
D ∞
Identify the value of
the lim 2 + (−0.1)n
n→∞
Section 11.1
Level: Easy
A 2
B 1
C DNE
D 0
Identify the value of
ln(n)
the lim
n→∞ ln(2n)
Section 11.1
Level: Hard
A ∞
B 0
C DNE
D 1
Consider the
following three
sequences:
an = (−1)n ,
bn = (−1)n /n,
cn = 2−n
A {an } and {bn }
converge; {cn }
diverges
Section 11.1
Level: Hard
B {an } and {cn }
converge; {bn }
diverges
C {an } and {cn }
Section 11.2
Level: Easy
True or False: If
lim an = 0 then
n→∞
∞
X
an converges.
n=0
A True
B False
Determine the
general term for the
following series
x4 x6 x8 x1 0
x+ + + +
+. . .
2 6 24 120
2xn
A
n!
x2n
B
n!
xn+2
C
(2n)!
2
Section 11.2
Level: Easy
D None of the
Which of the
following series are
geometric?
A 1 − 1/2 + 1/4 −
1/6 + . . .
Section 11.2
Level: Hard
B 2y − 6y 3 +
18y 5 − 54y 7 + . . .
C 1/2 + 2/3 +
3/4 + 4/5 + . . .
D x + x2 + x4 +
x7 + . . .
What is the∞value of
X (−1)n
the series
4n
n=0
Section N2
Level: Easy
1
4
4
B
5
C The series
doesn’t
converge
A
What is the formula
k
X
for
ari−1
i=1
Section N2
Level: Easy
A
a
1−r
a(1 − rk )
B
1−r
C The series
doesn’t
converge
Which of the
following is not an
example of
geometric growth?
A An endowment
Section N2
Level: Easy
B Earning annual
interest on an
account
C A population
doubling each
year
D All of the above
Which of the
following is a
correct
reindex of
∞
X
n
?
2n
−
1
n=1
Section N2
Level: Hard
∞
X
n−1
A
?
2n
−
3
n=2
∞
X
n−1
B
?
2n
−
2
n=2
∞
X
n+1
?
C
2n
+
1
n=2
Section N3
Level: Easy
For what values of
p does the series
∞
X
1
converge?
p
n
n=1
A p>1
B p<1
C p≥1
D p=1
Section N3
Level: Hard
True
or False
∞
X
1
1
=
n2
1 − (1/n2 )
n=1
A True
B False
Which series should
we
use to decide if
∞
X
1
converges
n
e
n=1
Section N3
Level: Easy
A
∞
X
1
n=1
n
?
∞
X
1
√ ?
B
n
n=1
∞
X
1
C
?
2
n
n=1
Which series should
we
use to decide if
∞
X
sin2 (n)
n3
n=1
converges
Section N3
Level: Easy
A
∞
X
1
n=1
n
?
∞
X
1
√ ?
B
n
n=1
∞
X
1
C
?
3
n
n=1
Which series should
we
use to decide if
∞
X
1
√
n+4
n=1
converges
Section N3
Level: Easy
A
∞
X
1
n=1
n
?
∞
X
1
√ ?
B
n
n=1
∞
X
1
C
?
2
n
n=1
Section 11.5
Level: Easy
In the statement of
the Ratio test
an+1
lim
= ρ we
n→∞ an
conclude
the series
P
an converges if
A ρ=1
B ρ 6= 1
C ρ>1
D ρ<1
Section 11.5
Level: Easy
Which of the
following is equal
to (n + 1)!
A n + 1 + n!
B (n + 1)n!
C nn + 1n
We can simplify
2n+1 to
Section 11.5
Level: Easy
A 2n + 1
B 2n + 2 1
C 2(2n )
Section 11.6
Level: Easy
We can rearrange
terms in a series
which does not
converge absolutely
so that the value of
the series equals
two different
values.
A True
B False
The
series
∞
X
(−1)n
Section 11.6
Level: Easy
n2
converges
absolutely
n=1
A True
B False
The
series
∞
X
(−1)n
Section 11.6
Level: Easy
n
converges
n=1
A True
B False
Section N4
Level: Easy
To compute the
interval of
convergence for a
power series you
use
A Integral Test
B Ratio Test
C Comparison Test
D Root Test
Section N4
Level: Easy
To express
9
as a
x3 + 3x2 − 4
power series our
first step is
A Differentiate
B Integrate
C Partial fractions
Section N4
Level: Easy
To express
1
as a
(x + 2)(x − 2)
power series our
first step is
A Integrate
B Partial Fractions
C Differentiate
Which of the
following is not a
power series?
A
Section N4
Level: Easy
∞
X
n=0
B
∞
X
1
n=0
C
1
(x − 5)n
n+1
∞
X
n=0
D x
n
(x − 5)n
1
(n − 5)n
n+1
Section N4
Level: Easy
To express ln(1 + x)
as a power series
our first step is
A Partial fractions
B Integrate
C Differentiate
Section N4
Level: Easy
To express atan(x)
as a power series
our first step is
A Partial fractions
B Integrate
C Differentiate
Section N4
Level: Easy
To
Z xexpress
1
dt as a
t
+
1
0
power series our
first step is
A Partial fractions
B Integrate
C Differentiate
1
(x + 2)2
as a power series
our first step is
To express
Section N4
Level: Easy
A Partial fractions
B Integrate
C Differentiate
If f (x) =
∞
X
n=0
Section 11.8
Level: Easy
what is f (0)
A c1 x
B 0
C c0
cn xn
Section 11.8
Level: Easy
The Taylor series for
f(x) centered at x=0
∞
X
f ( n)(0)xn
is
n!
n=0
A True
B False
−1
If f (x) = 1−x
then
(n)
f (x) =
Section 11.8
Level: Hard
A 0
B
(n)!
(1 − x)n+1
C
1
(1 − x)n+1
What is the
coefficient of x2 in
the Taylor series for
1
about a=0
(1 + x)2
Section 11.8
Level: Hard
1
6
1
B
3
C 1
A
D 3
E 6
A function f has the
following Taylor
series about a = 0
x4 x5 x6
xn+3
+ + +. . .+
+. . .
2! 3! 4!
(n + 1)!
Section 11.8
Level: Easy
A −3x sin(x) + 3x2
B − cos(x2 ) + 1
C −x2 cos(x) + x2
2
D ex − x2 − 1
E x2 ex − x3 − x2
Section 11.8
Level: Hard
Let
3x2 − 5x3 + 7x4 + 3x5
be the fifth-degree
Taylor polynomial
for the function f
about a=0. What is
the value of f (5) (0)
A -30
B 3 · 5!
C 0
D -5
E -15
Section 11.8
Level: Easy
The interval of
convergence for
sin(x) is
A −1 < x < 1
B 0<x<1
C −∞ < x < ∞
Section 11.8
Level: Easy
The interval of
convergence for
1
is
1−x
A −1 < x < 1
B 0<x<1
C −∞ < x < ∞
What is the power
series for sin(3x)
A
Section 11.9
Level: Easy
∞
X
(−1)n (3x)n
n=0
B
∞
X
(−1)n (3x)2n+1
n=0
C
n!
(2n + 1)!
∞
X
(−1)n (3x)2n
n=0
(2n)!
Section 11.9
Level: Easy
What is the power
2
series for ex
∞
X
(x)2n
A
n!
n=0
∞
X
((x)2n+1
B
(2n + 1)!
n=0
C
∞
X
(x)2n
n=0
(2n)!
What is the power
series for sin(x) − x
A
Section 11.9
Level: Hard
∞
X
(−1)n (x)n
n=1
B
∞
X
(−1)n (x)2n+1
n=1
C
n!
(2n + 1)!
∞
X
(−1)n (x)2n
n=1
(2n)!
∞
X
(−1)n 22n
Section 11.9
Level: Easy
is a
(2n)!
n=0
power series for
A e2
B sin(2)
C cos(2)
∞
X
(−1)n 2n x2n
Section 11.9
Level: Easy
is a
(n)!
n=0
power series for
A e−2x
2
B sin(2x2 )
C cos(2x2 )
Section 11.9
Level: Easy
If |f 0 (t)| < 1,
|f 00 (t)| < 2 and
|f 000 (t)| < 3 for t
with |t − 1| < 2 give
the bound on
|R2 (x)| on the
interval [−1, 3]
A 2·
23
3!
B 1·
23
3!
C 3·
23
3!
Section 11.9
Level: Hard
Which function is
larger for small x
(x < 1) by looking
at the first few
terms of their Taylor
Series
A 1 + sin(x)
B ex
Section 11.9
Level: Hard
Which function is
larger for small x
(x < 1) by looking
at the first few
terms of their Taylor
Series
1
A
1−x
B ex
(1 + x)m = where m
is not s positive
integer.
Section
11.10 Level:
Easy
A 1 + xm
B 1 + mx +
m(m−1)x2
+
2!
m(m−1)(m−2)x3
3!
...
+
Section
11.10 Level:
Easy
To solve the
differential
equation y 0 − y = x
with y(0) = 0 we
use a power series
of the form y =
a0 + a1 x + a2 x2 + . . ..
What is a0 ?
A 0
B 1
C 2
Which is the
general solution to
y 0 + ay = b + cx
A
Section
11.10 Level:
Easy
b
c
cx
− 2+
+
a −ax
a
a
Ce
a
B ( x (ab+b+acx)
+
a(a+1)
−a
C)x
a
C Ce− b+1 x
b+1
D C1 sin(x) +
C2 cos(x) + (b −
2d) + cx + dx2
Which is the
general solution to
xy 0 + ay = b + cx
A
Section
11.10 Level:
Easy
b
c
cx
− 2+
+
a −ax
a
a
Ce
a
B ( x (ab+b+acx)
+
a(a+1)
−a
C)x
a
C Ce− b+1 x
b+1
D C1 sin(x) +
C2 cos(x) + (b −
2d) + cx + dx2
Which is the
general solution to
y 0 + axb y = 0
A
Section
11.10 Level:
Easy
b
c
cx
− 2+
+
a −ax
a
a
Ce
a
B ( x (ab+b+acx)
+
a(a+1)
−a
C)x
a
C Ce− b+1 x
b+1
D C1 sin(x) +
C2 cos(x) + (b −
2d) + cx + dx2
Which is the
general solution to
y 00 + y = b + cx + dx2
A
Section
11.10 Level:
Easy
b
c
cx
− 2+
+
a −ax
a
a
Ce
a
B ( x (ab+b+acx)
+
a(a+1)
−a
C)x
a
C Ce− b+1 x
b+1
D C1 sin(x) +
C2 cos(x) + (b −
2d) + cx + dx2
Which is the
general solution to
y 00 − y = b + cx + dx2
A
Section
11.10 Level:
Easy
b
c
cx
− 2+
+
a −ax
a
a
Ce
a
B ( x (ab+b+acx)
+
a(a+1)
−a
C)x
a
C Ce− b+1 x
b+1
D C1 sin(x) +
C2 cos(x) + (b −
2d) + cx + dx2
If y = f (t) and
x = g(t) what is
Section 3.5
Level: Easy
A
f 0 (t)
g 0 (t)
g 0 (t)
B
f 0 (t)
f 00 (t)
C
g 0 (t)
dy
dx
Section36.eps Is a
graph of which
parametric
equation?
Section 3.5
Level: Easy
A x(t) = t
y = (t) = sin(t)
B x(t) = cos(t)
y=t
√
C x(t) = √1 − t2
y(t) = 1 − t2
D x(t) = cos(t)
y(t) = sin(t)
The formula for the
length of a
parametric curve
with x = f (t),
y = g(t) is
Z bp
A
1 + f 0 (t)dt
Section 6.3
Level: Easy
a
B
Z bp
1 + (f 0 (t))2 dt
a
C
Z bp
f 0 (t) + g 0 (t)dt
a
Section 10.5
Level: Easy
Which polar
coordinate is the
same as the
rectangular
coordinate (3, 0)
A (3, 0)
B (3, π)
C (3, π/2)
Section 10.5
Level: Easy
Which rectangular
coordinate is the
same as (−3, π)
A (3, 0)
B (3, π)
C (3, π/2)
Section 10.5
Level: Easy
Which cartesian
equation is the
same as r = 4 csc(θ)
A y=4
B x=4
C y=
1
4
Section 10.5
Level: Easy
Which polar
equation is the
same as x2 + y 2 = 2
A sin(θ) = 2
B csc(θ) = 2
C r2 = 2
Section 10.6
Level: Hard
The points of
intersection for
r = 1 + cos(θ) and
r = 1 − cos(θ)
A (1, 0), (1, π)
B (1, π2 ), (1, 3π
2 )
C (0, 0)
Section 10.6
Level: Hard
The points of
intersection for
r = 1 + sin(θ) and
r = 1 − sin(θ)
A (1, 0), (1, π),
(0, 0)
B (1, π2 ), (1, 3π
2 )
C (2, 0)
Section 10.6
Level: Easy
Which describes
the graph of the
equation
r sin(θ) = 10?
A Line
B Circle
C Spiral
D Rose
Which describes
the graph of the
equation r = θ?
Section 10.6
Level: Easy
A Line
B Circle
C Spiral
D Rose
With sθ = sin(θ)
and cθ = cos(θ), the
arc length of
r = 4 cos(θ) is
A
π/2 p
Z
(−4sθ)2 + (4cθ)2 dθ
0
B
Z
Section 10.7
Level: Easy
2
π/2 p
(−4sθ)2 + (4cθ)2 d
0
C
Z
2
0
π
p
(−4sθ)2 + (4cθ)2 dθ
Z
Section 10.7
Level: Easy
β
r
dr 2
) dθ
dθ
α
is the length of a
polar curve from α
to β
r2 + (
A True
B False
The formula for the
area in one leaf of
r = cos(2θ) is
Section107.eps
Z π/2
A
cos(2θ)dθ
Section 10.7
Level: Easy
−π/2
B
π/3
Z
cos(2θ)dθ
−π/3
C
π/4
Z
cos(2θ)dθ
−π/4
D
Z
π
cos(2θ)dθ
0
Area shared by
r = 2 and
r = 2(1 − c(θ)) is
Section1072.eps
A
Section 10.7
Level: Hard
2π
Z
0
B
1
(2(1 − c(θ))2 − 22 dθ
2
Z
π/2
Z
π/2
1
(2(1 − c(θ))2 + 4πd
−π/2 2
2
C
2
2π
0
1
(2(1 − c(θ))2 dθ+
2
Write
form
Section A.5
Level: Easy
2+i
in a + bi
1−i
A 2 − 1i
(2 + i)(1 + i)
=
B
(1 − i)(1 + i)
1 + 3i
2
2
i
C
+
1−i 1−i
Euler’s formula says
eiθ =
Section A.5
Level: Easy
A cos(θ) + i sin(θ)
B sin(θ) + i cos(θ)
C ei eθ
Section A.5
Level: Easy
Which of the
following is equal
to 2eiπ/3
√
A
3+i
√
B 1 − 3i
√
C 1 + 3i
Section A.5
Level: Easy
Which of the
following is equal
to 1 + i
A 2eiπ/3
√ iπ/4
B
2e
C eiπ/4
How many complex
numbers are a
solution to
x100 − 1 = 0
Section A.5
Level: Easy
A 1
B 2
C 50
D 99
E 100
Section A.5
Level: Easy
How many real
solutions does
x3 = 1 have?
A 1
B 2
C 3
cosh(x) =
Section 7.8
Level: Easy
ex − e−x
A
2
ex + e−x
B
2
C cos(x)
sinh(x) =
Section 7.8
Level: Easy
ex − e−x
A
2
ex + e−x
B
2
C sin(x)