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Duplicate of Calculus BC AP Test Review
ln(ab)=
Which is not a way to decide whether a series diverges?
Duplicate of Calculus BC AP Test Review
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Calculus BC Review for AP Test
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Answers
1
Which is not a way to decide whether a series diverges?
determining the sequence converges
integral test
limit comparison
root test
2
ln(ab)=
ln(a) + ln(b)
ln(a) - ln(b)
b×ln(a)
ln(a+b)
3
If a function has an inverse it must...
be continuous
have endpoints
be differentiable
be one-to-one
4
d/dx log
a
x=
1/ax
1/(xln(a))
1/ln(a)
a/ln(x)
5
If f'(c) exists and does not equal zero then
f(c) = f-1(c)
f-1(c) exists
f'(c) = f-1(c)
f-1 is differentiable at f(c)
6
Which correctly describes the natural log function?
Domain (0,∞), Range (-∞,∞), One-to-one, concave up
Domain (0,∞), Range (-∞,∞), One-to-one, concave down
Domain (-∞,∞), Range (-∞,∞), One-to-one, concave up
Domain (0,∞), Range (-∞,0), One-to-one, concave down
7
d/dx(ln|u|)=
u'/u
u
1/u
u'
8
If f is increasing, f
-1
is
decreasing
increasing
concave up
concave down
9
∫1/√(a
2
-u
2
) du=
arcsin(u/a) +c
1/a×arcsec(u/a) +c
arcsin(u) +c
1/a×arcsin(u/a) +c
10
d/dx(a
x
)=
ln<font size="2">(ax)</font>
ln(a)×ax
a/ln(x)
1/ln(a)
11
∫sin(u) du=
sin(u) +c
cos(u) +c
-cos(u) +c
-sin(u) +c
12
d/dx arcsin(u)=
u'/√(1-u2)
u'/(1-u2)
u'/(1+u2)
u'/√(1+u2)
13
Definition of a Continuous Function
f(c) is defined
limx->c f(x)= f(c)
no holes, jumps or asymptotes
limx->c f(x) exists
14
The area within a polar graph is defined by
π∫f(θ)2
∫f(θ)2
1/2×∫f(θ)2
∫f(θ)
15
Which of these represents volume of revolution by washers?
V=∫R2-r2
V=∫R2
V=π∫R2
V=π∫R2-r2
16
log
a
x=
1/ln(a)×ln(x)
1/ln(a)
aln(x)
xln(a)
17
∫a
x
dx=
ax/x +c
ax/ln(a) +c
1/ax +c
ax +c
18
∫1/(u√(u
2
-a
2
)) du=
1/a×arcsin(u/a) +c
arcsin(u) +c
1/a×arcsec(∣u∣/a) +c
arcsin(u/a) +c
19
To solve ∫1/(x
2
-5x+6) dx you should use
Limit Comparirson
U-Substitution
It cannot be solved
Partial Fractions
20
∫cot(u) du=
-∣u∣ +c
ln∣sin(u)∣ +c
sin(u) +c
-ln∣sin(u)∣ +c
21
d/dx arcsec(x)=
u'/√(u2+1)
u'/(∣u∣√(u2-1))
u'/(∣u∣√(u2+1))
u'/√(u2-1)
22
Most important thing to remember by the AP test
riemann sums
hidden derivatives
chain rule
+c
23
d/dx arctan(u)=
u'/√(1+u2)
u'/(1+u2)
u'/(1-u2)
u'/√(1-u2)
24
ln(a
n
)=
n×ln(a)
ln(a) + ln(n)
ln(a)×ln(n)
n + ln(a)
25
If f
-1
contains the point (a,b), then...
f contains the point (b,a)
f contains the point (-a,b)
f contains the point (-a,-b)
f contains the point (a,b)
26
What is the definition of an inverse function?
f(g(x)) = g(f(x)) = x
f(x) × g(x) = x
f(g(x)) = x
f(g(x)) = g(f(x))
27
∫1/x dx=
1/x+c
lnx+c
x+c
0
28
What information do you need to do Euler's method?
A point, ∆x, and an f' function
A point and several derivatives
A point, ∆x, and corresponding derivatives
A point and a ∆x
29
Which function represents logistic growth?
y=L/(1+be-kt)
y=L/(1-bekt)
y=L/(1+bekt)
y=L/(1-be-kt)
30
The remainder of a Taylor polynomial is always less than the absolute value of the next term
True
False
31
∫tan(u) du=
∣cos(u)∣ +c
-ln(u) +c
-ln∣cos(u)∣ +c
-ln(cos(u)) +c
32
a
x
=
eln(a)x
aln(x)
xlog(e)
xln(a)
33
If f is continuous, then
f-1 is continuous
f-1 is monatonic
nothing can be concluded about f-1
f-1 is differentiable
34
ln(1)=
∞
1
0
e
35
∫1/(a
2
+u
2
) du=
1/a×arcsin(u/a) +c
arctan(u/a) +c
1/a×arctan(u/a) +c
arcsin(u/a) +c
36
∫sec(u) du=
ln∣sec(u) + tan(u)∣ +c
ln∣sec(u)tan(u)∣ +c
-ln∣sec(u)∣ +c
-sec(u) + tan(u) +c
37
∫csc(u) du=
-csc(u) + cot(u) +c
-∣csc(u) + cot(u)∣ +c
-ln∣csc(u) + cot(u)∣ +c
ln∣csc(u) + cot(u)∣ +c
38
What does not have to be true for the alternating series test to apply?
first term is less than 1
alternates
sequence goes to 0
always decreasing
39
∫u dv=
u×v+∫v du
u+v-∫v du
-∫v du
u×v-∫v du
40
f'(x) is defined by the function y=2x+3 and f passes through the point (1,7). What is f(x)?
y=2x+6
y=x2+3x
y=x2+3x+3
y=x2+3x+7
41
L'Hopital's rule
applies only when you get 0/0 while solving a limit
always works
Can only be used once per problem
Is not a real calculus concept
42
∫cos(u) du=
sin(u) +c
-cos(u) +c
-sin(u) +c
cos(u) +c
43
If f and g are inverses, then g'(x)=
-f'(x)
1/f'(g(x))
1/f'(x)
-1/f'(x)
44
If y'=ky, then
y=Cet
y=Cekt
y=et
y=ekt
45
∫√(1+f'(x)
2
) represents
Derivative
Arclength
A Parabola
Net Distance
