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Ch 7 Review
d/dx arcsec(x)=
∫1/√(a2-u2) du=
Ch 7 Review
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Calculus BC Review for AP Test
Flashcards
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Questions
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Answers
1
∫1/√(a
2
-u
2
) du=
1/a×arcsin(u/a) +c
arcsin(u) +c
arcsin(u/a) +c
1/a×arcsec(u/a) +c
2
d/dx arcsec(x)=
u'/(∣u∣√(u2-1))
u'/√(u2-1)
u'/(∣u∣√(u2+1))
u'/√(u2+1)
3
To solve ∫1/(x
2
-5x+6) dx you should use
Partial Fractions
It cannot be solved
Limit Comparirson
U-Substitution
4
ln(1)=
∞
1
e
0
5
ln(a
n
)=
ln(a) + ln(n)
ln(a)×ln(n)
n×ln(a)
n + ln(a)
6
∫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
7
The remainder of a Taylor polynomial is always less than the absolute value of the next term
True
False
8
Which of these represents volume of revolution by washers?
V=π∫R2-r2
V=∫R2
V=π∫R2
V=∫R2-r2
9
log
a
x=
1/ln(a)×ln(x)
aln(x)
1/ln(a)
xln(a)
10
d/dx(a
x
)=
ln<font size="2">(ax)</font>
a/ln(x)
1/ln(a)
ln(a)×ax
11
∫√(1+f'(x)
2
) represents
Arclength
Derivative
Net Distance
A Parabola
12
∫cos(u) du=
-cos(u) +c
-sin(u) +c
sin(u) +c
cos(u) +c
13
d/dx arcsin(u)=
u'/(1+u2)
u'/(1-u2)
u'/√(1-u2)
u'/√(1+u2)
14
∫csc(u) du=
-∣csc(u) + cot(u)∣ +c
-ln∣csc(u) + cot(u)∣ +c
ln∣csc(u) + cot(u)∣ +c
-csc(u) + cot(u) +c
15
If a function has an inverse it must...
be one-to-one
have endpoints
be differentiable
be continuous
16
If y'=ky, then
y=ekt
y=Cekt
y=et
y=Cet
17
Most important thing to remember by the AP test
+c
hidden derivatives
riemann sums
chain rule
18
What does not have to be true for the alternating series test to apply?
always decreasing
sequence goes to 0
alternates
first term is less than 1
19
∫tan(u) du=
-ln∣cos(u)∣ +c
-ln(cos(u)) +c
∣cos(u)∣ +c
-ln(u) +c
20
If f is continuous, then
nothing can be concluded about f-1
f-1 is continuous
f-1 is differentiable
f-1 is monatonic
21
∫1/x dx=
lnx+c
0
x+c
1/x+c
22
∫a
x
dx=
ax/ln(a) +c
ax/x +c
ax +c
1/ax +c
23
ln(ab)=
ln(a) + ln(b)
ln(a+b)
b×ln(a)
ln(a) - ln(b)
24
∫1/(u√(u
2
-a
2
)) du=
arcsin(u) +c
1/a×arcsec(∣u∣/a) +c
1/a×arcsin(u/a) +c
arcsin(u/a) +c
25
∫sec(u) du=
-ln∣sec(u)∣ +c
-sec(u) + tan(u) +c
ln∣sec(u) + tan(u)∣ +c
ln∣sec(u)tan(u)∣ +c
26
What is the definition of an inverse function?
f(g(x)) = g(f(x)) = x
f(g(x)) = g(f(x))
f(x) × g(x) = x
f(g(x)) = x
27
If f'(c) exists and does not equal zero then
f-1 is differentiable at f(c)
f'(c) = f-1(c)
f-1(c) exists
f(c) = f-1(c)
28
Which function represents logistic growth?
y=L/(1-bekt)
y=L/(1+bekt)
y=L/(1-be-kt)
y=L/(1+be-kt)
29
L'Hopital's rule
Is not a real calculus concept
Can only be used once per problem
applies only when you get 0/0 while solving a limit
always works
30
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=x2+3x
y=2x+6
31
If f
-1
contains the point (a,b), then...
f contains the point (-a,b)
f contains the point (b,a)
f contains the point (a,b)
f contains the point (-a,-b)
32
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 (-∞,∞), One-to-one, concave down
Domain (0,∞), Range (-∞,0), One-to-one, concave down
33
If f and g are inverses, then g'(x)=
1/f'(g(x))
-1/f'(x)
1/f'(x)
-f'(x)
34
d/dx log
a
x=
1/ax
1/(xln(a))
a/ln(x)
1/ln(a)
35
Definition of a Continuous Function
limx->c f(x) exists
f(c) is defined
limx->c f(x)= f(c)
no holes, jumps or asymptotes
36
d/dx arctan(u)=
u'/(1+u2)
u'/(1-u2)
u'/√(1+u2)
u'/√(1-u2)
37
If f is increasing, f
-1
is
decreasing
concave down
concave up
increasing
38
∫cot(u) du=
-∣u∣ +c
sin(u) +c
-ln∣sin(u)∣ +c
ln∣sin(u)∣ +c
39
Which is not a way to decide whether a series diverges?
root test
integral test
limit comparison
determining the sequence converges
40
∫u dv=
u+v-∫v du
-∫v du
u×v+∫v du
u×v-∫v du
41
What information do you need to do Euler's method?
A point, ∆x, and an f' function
A point, ∆x, and corresponding derivatives
A point and several derivatives
A point and a ∆x
42
a
x
=
aln(x)
xlog(e)
xln(a)
eln(a)x
43
The area within a polar graph is defined by
1/2×∫f(θ)2
∫f(θ)2
π∫f(θ)2
∫f(θ)
