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