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Duplicate of Calculus BC AP Test Review
∫1/(a2+u2) du=
d/dx(ax)=
Duplicate of Calculus BC AP Test Review
45 terms
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Calculus BC Review for AP Test #calculusbc #bc #calculus #apcalculus
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Answers
1
d/dx(a
x
)=
ln<font size="2">(ax)</font>
a/ln(x)
ln(a)×ax
1/ln(a)
2
∫1/(a
2
+u
2
) du=
arcsin(u/a) +c
1/a×arcsin(u/a) +c
arctan(u/a) +c
1/a×arctan(u/a) +c
3
∫cos(u) du=
sin(u) +c
-cos(u) +c
cos(u) +c
-sin(u) +c
4
Which function represents logistic growth?
y=L/(1+be-kt)
y=L/(1+bekt)
y=L/(1-be-kt)
y=L/(1-bekt)
5
d/dx(ln|u|)=
u'/u
u
u'
1/u
6
If f and g are inverses, then g'(x)=
-f'(x)
1/f'(x)
1/f'(g(x))
-1/f'(x)
7
If a function has an inverse it must...
be continuous
have endpoints
be one-to-one
be differentiable
8
L'Hopital's rule
always works
Can only be used once per problem
Is not a real calculus concept
applies only when you get 0/0 while solving a limit
9
∫1/x dx=
lnx+c
0
1/x+c
x+c
10
∫tan(u) du=
∣cos(u)∣ +c
-ln∣cos(u)∣ +c
-ln(cos(u)) +c
-ln(u) +c
11
∫sin(u) du=
-cos(u) +c
-sin(u) +c
cos(u) +c
sin(u) +c
12
∫√(1+f'(x)
2
) represents
Arclength
Net Distance
Derivative
A Parabola
13
∫sec(u) du=
-sec(u) + tan(u) +c
ln∣sec(u) + tan(u)∣ +c
-ln∣sec(u)∣ +c
ln∣sec(u)tan(u)∣ +c
14
Which of these represents volume of revolution by washers?
V=∫R2-r2
V=π∫R2
V=∫R2
V=π∫R2-r2
15
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)
16
If f is continuous, then
f-1 is differentiable
f-1 is continuous
f-1 is monatonic
nothing can be concluded about f-1
17
If f is increasing, f
-1
is
concave up
increasing
decreasing
concave down
18
The remainder of a Taylor polynomial is always less than the absolute value of the next term
True
False
19
If f'(c) exists and does not equal zero then
f'(c) = f-1(c)
f-1 is differentiable at f(c)
f(c) = f-1(c)
f-1(c) exists
20
∫1/√(a
2
-u
2
) du=
1/a×arcsin(u/a) +c
arcsin(u) +c
1/a×arcsec(u/a) +c
arcsin(u/a) +c
21
a
x
=
xlog(e)
eln(a)x
xln(a)
aln(x)
22
ln(ab)=
ln(a) + ln(b)
ln(a+b)
ln(a) - ln(b)
b×ln(a)
23
d/dx arcsin(u)=
u'/(1+u2)
u'/(1-u2)
u'/√(1+u2)
u'/√(1-u2)
24
∫u dv=
u×v+∫v du
u×v-∫v du
-∫v du
u+v-∫v du
25
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+7
y=x2+3x
y=2x+6
y=x2+3x+3
26
Most important thing to remember by the AP test
hidden derivatives
riemann sums
chain rule
+c
27
Which is not a way to decide whether a series diverges?
determining the sequence converges
root test
limit comparison
integral test
28
d/dx arctan(u)=
u'/(1+u2)
u'/√(1-u2)
u'/√(1+u2)
u'/(1-u2)
29
What does not have to be true for the alternating series test to apply?
always decreasing
alternates
first term is less than 1
sequence goes to 0
30
log
a
x=
xln(a)
aln(x)
1/ln(a)
1/ln(a)×ln(x)
31
∫a
x
dx=
ax +c
ax/ln(a) +c
1/ax +c
ax/x +c
32
ln(a
n
)=
ln(a) + ln(n)
ln(a)×ln(n)
n×ln(a)
n + ln(a)
33
The area within a polar graph is defined by
1/2×∫f(θ)2
∫f(θ)2
∫f(θ)
π∫f(θ)2
34
∫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
35
Which correctly describes the natural log function?
Domain (-∞,∞), Range (-∞,∞), One-to-one, concave up
Domain (0,∞), Range (-∞,∞), One-to-one, concave down
Domain (0,∞), Range (-∞,0), One-to-one, concave down
Domain (0,∞), Range (-∞,∞), One-to-one, concave up
36
If y'=ky, then
y=et
y=Cet
y=Cekt
y=ekt
37
What is the definition of an inverse function?
f(x) × g(x) = x
f(g(x)) = g(f(x)) = x
f(g(x)) = g(f(x))
f(g(x)) = x
38
ln(1)=
0
e
1
∞
39
∫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
40
∫cot(u) du=
sin(u) +c
-ln∣sin(u)∣ +c
-∣u∣ +c
ln∣sin(u)∣ +c
41
Definition of a Continuous Function
limx->c f(x)= f(c)
limx->c f(x) exists
f(c) is defined
no holes, jumps or asymptotes
42
d/dx arcsec(x)=
u'/√(u2+1)
u'/(∣u∣√(u2-1))
u'/√(u2-1)
u'/(∣u∣√(u2+1))
43
d/dx log
a
x=
a/ln(x)
1/ax
1/ln(a)
1/(xln(a))
44
To solve ∫1/(x
2
-5x+6) dx you should use
Partial Fractions
It cannot be solved
Limit Comparirson
U-Substitution
45
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 a ∆x
A point and several derivatives
