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Duplicate of AP Calculus Formula_2
Duplicate of AP Calculus Formula_2
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AP Calculus Formulas to Know & Understand
Flashcards
38 cards
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Practice quiz
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Questions
38
Answers
1
Complete:
concavity
maximum
slope
minimum
2
Find the derivative:
u'v-uv'
u'+v'
(uv)n-1
uv'+u'v
3
Find the derivative:
-sinx
sin2x
sinx
-cscxcosx
4
a(t)=
x'(t)
x(t)
v'(t)
v(t)
5
The following formulas are used to represent the _________________.
average time
average acceleration
change in position
average rate of change or average velocity
6
A limit exists when there is a
jump
hole
oscillation
vertical asympotote
7
All critical points are either a max or a min.
True
False
8
d/dx(arctanx)
1/(√(x2-1)
-1/(1+x2)
1/(1+x2)
-1/(√(x2-1)
9
Find the derivative:
sec2x
secxtanx
cscxtanx
tan2x
10
Find the derivative:
secx
sec2x
csc2x
sinx/cosx
11
The following formula represents the...
definition of the derivative at x=a
"easy" way to calculate a derivative
definition of derivative
Fundamental Theorem of Calculus
12
Find the derivative:
u'v-uv'
u'v+uv'
(u'v+v'u)/(v2)
(u'v-v'u)/(v2)
13
Find the derivative:
-csc2x
-sec2x
-cosx
-cscxcotx
14
Which does the integral equal?
-cscx+C
cscx+C
-cotx+C
cotx+C
15
What does the integral equal?
aulna+C
au/lna+C
ln|u|+C
1/ulna+C
16
d/dx(e
x
)
ex/lna
1/x
exlna
ex
17
Find the derivative:
nx
nxn
nxn-1
(n-1)xn-1
18
The MVT is where the slope of the secant line is equal to the
acceleration
inverse
slope of the normal line
slope of the tangent line
19
v(t)=
a'(t)
x'(t)
x(t)
a(t)
20
Find the derivative:
-sinx
cos2x
cosx
-cosx
21
d/dx(a
x
)=
ax/lna
ax
axlna
1/x
22
The following formula represents the...
slope field
average value
definition of derivate
average rate of change
23
A particle changes direction when
a(t)=0
v(t)=0
x(t)=0
v(t) crosses the t-axis
24
d/dx(lnx)
1/(xlna)
ex
x
1/x
25
The formula given represents
average acceleration of a particle
average velocity of a particle
the displacement of a particle
the total distance traveled of a particle
26
d/dx(arccosx)
1/(1+x2)
-1/(√(1-x2)
-1/(1+x2)
1/(√(1-x2)
27
A POI is when f ''(x)=0.
True
False
28
What does the integral equal?
arcsin(u/a)+c
(1/a)arcsec(u/a)+c
(1/a)arctan(u/a)+c
29
A particle slows down when v(t) and a(t) are
are the same sign
different signs
30
Find the derivative:
-sec2x
-cscxcotx
-csc2x
secx
31
Evaluate the limit. lim
x->0
(1-cosx)/x
1
0
∞
DNE
32
The extreme value theorem says if a function is differential from [a,b] there will be an
absolute min
absolute max
none of the above
absolute min and an absolute max
33
What does the integral equal?
aulna
1/u
au/lna
1/ulna
34
The formula given represents
the displacement of a particle
average velocity of a particle
average acceleration of a particle
the total distance traveled of a particle
35
A derivative fails to exist when there is a
all of them
cusp
corner
vertical tangent
36
The theorem shown in the picture is the
extreme value theorem
mean value theorem
average value theorem
FTC
37
Evaluate the limit. lim
x->0
sinx/x
DNE
∞
0
1
38
The FTC does which of the following
finds extrema
says derivatives and integrals undo each other
finds exact area under a curve
connects position and acceleration
