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

A point, ∆x, and corresponding derivatives

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

determining the sequence converges

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

Most important thing to remember by the AP test

hidden derivatives, +c, chain rule, riemann sums

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

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Duplicate of Calculus BC AP Test Review

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

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Questions 36

Answers

1
What does not have to be true for the alternating series test to apply?
first term is less than 1
alternates
always decreasing
sequence goes to 0
2
∫1/x dx=
x+c
0
1/x+c
lnx+c
3
∫1/√(a²-u²) du=
arcsin(u) +c
arcsin(u/a) +c
1/a×arcsin(u/a) +c
1/a×arcsec(u/a) +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 arcsin(u)=
u'/√(1+u2)
u'/(1+u2)
u'/√(1-u2)
u'/(1-u2)
6
∫1/(a²+u²) du=
arcsin(u/a) +c
1/a×arctan(u/a) +c
arctan(u/a) +c
1/a×arcsin(u/a) +c
7
What information do you need to do Euler's method?
A point and a ∆x
A point, ∆x, and corresponding derivatives
A point and several derivatives
A point, ∆x, and an f' function
8
∫cos(u) du=
sin(u) +c
-sin(u) +c
-cos(u) +c
cos(u) +c
9
∫tan(u) du=
∣cos(u)∣ +c
-ln∣cos(u)∣ +c
-ln(cos(u)) +c
-ln(u) +c
10
To solve ∫1/(x²-5x+6) dx you should use
U-Substitution
It cannot be solved
Limit Comparirson
Partial Fractions
11
∫cot(u) du=
-ln∣sin(u)∣ +c
-∣u∣ +c
ln∣sin(u)∣ +c
sin(u) +c
12
The area within a polar graph is defined by
1/2×∫f(θ)2
π∫f(θ)2
∫f(θ)2
∫f(θ)
13
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
14
d/dx(a^x)=
ln(a)×ax
ln<font size="2">(ax)</font>
1/ln(a)
a/ln(x)
15
∫csc(u) du=
ln∣csc(u) + cot(u)∣ +c
-∣csc(u) + cot(u)∣ +c
-ln∣csc(u) + cot(u)∣ +c
-csc(u) + cot(u) +c
16
Which is not a way to decide whether a series diverges?
limit comparison
root test
determining the sequence converges
integral test
17
d/dx arctan(u)=
u'/√(1-u2)
u'/(1+u2)
u'/√(1+u2)
u'/(1-u2)
18
∫√(1+f'(x)²) represents
Derivative
Arclength
A Parabola
Net Distance
19
If f is continuous, then
f-1 is continuous
f-1 is differentiable
nothing can be concluded about f-1
f-1 is monatonic
20
∫1/(u√(u²-a²)) du=
arcsin(u/a) +c
arcsin(u) +c
1/a×arcsin(u/a) +c
1/a×arcsec(∣u∣/a) +c
21
ln(aⁿ)=
n×ln(a)
n + ln(a)
ln(a) + ln(n)
ln(a)×ln(n)
22
If f is increasing, f^-1 is
increasing
concave up
concave down
decreasing
23
∫sec(u) du=
ln∣sec(u)tan(u)∣ +c
-sec(u) + tan(u) +c
ln∣sec(u) + tan(u)∣ +c
-ln∣sec(u)∣ +c
24
∫a^x dx=
1/ax +c
ax/x +c
ax/ln(a) +c
ax +c
25
If a function has an inverse it must...
be one-to-one
be continuous
be differentiable
have endpoints
26
L'Hopital's rule
Can only be used once per problem
applies only when you get 0/0 while solving a limit
always works
Is not a real calculus concept
27
If f'(c) exists and does not equal zero then
f(c) = f-1(c)
f'(c) = f-1(c)
f-1(c) exists
f-1 is differentiable at f(c)
28
The remainder of a Taylor polynomial is always less than the absolute value of the next term
True
False
29
If f^-1contains the point (a,b), then...
f contains the point (a,b)
f contains the point (-a,b)
f contains the point (b,a)
f contains the point (-a,-b)
30
Which of these represents volume of revolution by washers?
V=∫R2
V=∫R2-r2
V=π∫R2
V=π∫R2-r2
31
Most important thing to remember by the AP test
hidden derivatives
+c
chain rule
riemann sums
32
d/dx log_ax=
1/ln(a)
1/ax
1/(xln(a))
a/ln(x)
33
If y'=ky, then
y=et
y=Cet
y=ekt
y=Cekt
34
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
35
∫u dv=
-∫v du
u×v+∫v du
u×v-∫v du
u+v-∫v du
36
∫sin(u) du=
sin(u) +c
-sin(u) +c
-cos(u) +c
cos(u) +c

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