What information do you need to do Euler's method?

A point, ∆x, and corresponding derivatives

Definition of a Continuous Function

limx->c f(x) exists, no holes, jumps or asymptotes, f(c) is defined, limx->c f(x)= f(c)

Which is not a way to decide whether a series diverges?

determining the sequence converges

Which correctly describes the natural log function?

Domain (0,∞), Range (-∞,∞), One-to-one, concave down

applies only when you get 0/0 while solving a limit

Most important thing to remember by the AP test

+c, chain rule, riemann sums, hidden derivatives

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Calculus BC Review for AP Test #calculusbc #bc #calculus #apcalculus

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Questions 45

Answers

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

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