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Study sets matching "calculus ab"

62 terms
Calculus AB
1
0
Squeeze Theorem
f is continuous at x=c if...
1
0
39 terms
Calculus AB
average value
mean value theorem
d/dx [lul]
d/dx [ln u]
u'u/lul
u'/u
average value
mean value theorem
17 terms
AB Calculus
Derivative of a Constant Function
Power Rule for Positive Integers
The Constant Multiple Rule (POTC)
The Sum + Difference Rule
If f is the function with a constant value c, then df/dx = d'…
If n is an integer and x cannot equal 0,
Pull out the multiplicative constant
Derivative of a Constant Function
If f is the function with a constant value c, then df/dx = d'…
Power Rule for Positive Integers
If n is an integer and x cannot equal 0,
48 terms
Calculus AB
Slope (know x1,x1,y1,y2)
Point-slope equation
Slope-intercept equation
General Linear equation
m = Δy/Δx = (y2-y1)/(x2-x1)
y=m(x-x1) +y1
y=mx + b
Ax+By = C
Slope (know x1,x1,y1,y2)
m = Δy/Δx = (y2-y1)/(x2-x1)
Point-slope equation
y=m(x-x1) +y1
73 terms
Calculus AB
exponential function
indefinite integral
Absolute minimum
Differentiable
A function of the form f (x) = a x where a is any positive co…
this represents the family of antiderivatives of the function f
The least single value that a function attains on a given int…
A function f is said to be differentiable at a point x = a if…
exponential function
A function of the form f (x) = a x where a is any positive co…
indefinite integral
this represents the family of antiderivatives of the function f
65 terms
AP Calculus AB Formulas
Definition of Derivative
Alternate Definition of Derivative
Volume using Disks
Volume using Washers
Definition of Derivative
Alternate Definition of Derivative
36 terms
AB Calculus
Numerical derivative on calculator por…
Rounding
Justification
state when, what, how, and how much
does not require work to be shown
Round to 3 decimals at the end, 5 during work
use what has been given to you
state when, what, how, and how much
Numerical derivative on calculator por…
does not require work to be shown
65 terms
AP Calculus AB Formulas
Definition of Derivative
Alternate Definition of Derivative
Volume using Disks
Volume using Washers
Definition of Derivative
Alternate Definition of Derivative
63 terms
AP AB Calculus Flash Cards
1
0
f is continuous at x=c if...
Intermediate Value Theorem
If f is continuous on [a,b] and k is a number between f(a) an…
1
0
67 terms
AP Calculus AB Exam
Intermediate Value Theorem
Average Rate of Change
Instantenous Rate of Change
Formal definition of derivative
If f(1)=-4 and f(6)=9, then there must be a x-value between 1…
Slope of secant line between two points, use to estimate inst…
Slope of tangent line at a point, value of derivative at a po…
limit as h approaches 0 of [f(a+h)-f(a)]/h
Intermediate Value Theorem
If f(1)=-4 and f(6)=9, then there must be a x-value between 1…
Average Rate of Change
Slope of secant line between two points, use to estimate inst…
16 terms
AP Calculus AB - Derivatives
Derivative of sin(x)
Derivative of cos(x)
Derivative of tan(x)
Derivative of csc(x)
Derivative of sin(x)
Derivative of cos(x)
20 terms
Calculus AB AP - Limit Practice
10
5
6
3/2
Evaluate the limit in Part A given the following information:
Evaluate the limit in Part B given the following information:
Evaluate the limit in Part C given the following information:
Evaluate the limit in Part D given the following information:
10
Evaluate the limit in Part A given the following information:
5
Evaluate the limit in Part B given the following information:
17 terms
Calculus AB
Absolute maximum
Acceleration
Average Rate of Change
Concave Down
The greatest single value that a function attains on a given…
The rate of change of velocity.
For a function f (x) , this represents the total change in f…
A term applied to a section of the graph where the derivative…
Absolute maximum
The greatest single value that a function attains on a given…
Acceleration
The rate of change of velocity.
20 terms
Calculus AB
Intermediate Value Theorem
Mean Value Theorem
Fundamental Theorem of Calculus #1
FTC #2
What Theorem covers this?... If f is continuous on [a,b] and k…
Name this Theorem
What is Theorem called?... The definite integral of a rate of c…
What is this called?
Intermediate Value Theorem
What Theorem covers this?... If f is continuous on [a,b] and k…
Mean Value Theorem
Name this Theorem
45 terms
Calculus AB
d/dx sin(u)
d/dx cos(u)
d/dx cot(u)
d/dx tan(u)
cos(u)u'
-sin(u)u'
-csc^2(u)u'
sec^2(u)u'
d/dx sin(u)
cos(u)u'
d/dx cos(u)
-sin(u)u'
5 terms
AB Calculus
Derivative of sin(x)
Derivative of tan
Derivative of cos
Derivative of cot
Cos(x)
Sec^2
-sin
-csc^2
Derivative of sin(x)
Cos(x)
Derivative of tan
Sec^2
6 terms
Calculus AB
D/dx SinX
D/dx Cosx
D/dx Tanx
D/dx Cscx
Cosx
-Sinx
Sec^2x
-CscxCotx
D/dx SinX
Cosx
D/dx Cosx
-Sinx
12 terms
AB Calculus
dy/dx sinx
dy/dx cosx
dy/dx tanx
dy/dx secx
cosx
-sinx
sec^2x
secxtanx
dy/dx sinx
cosx
dy/dx cosx
-sinx
10 terms
Calculus AB
Intermediate Value Theorem
Mean Value Theorem
Rolle's Theorem
Trig Identity: sin2x =
If the function f(x) is continuous on [a,b], and 'y' is a num…
If the function f(x) is continuous on [a,b], AND the first de…
If the function f(x) is continuous on [a,b], AND the first de…
2sin(x)cos(x)
Intermediate Value Theorem
If the function f(x) is continuous on [a,b], and 'y' is a num…
Mean Value Theorem
If the function f(x) is continuous on [a,b], AND the first de…
25 terms
Calculus AB
sin 2x
(sin x)^2 + (cos x)^2
(tan x)^2 + 1
1 + (cot x)^2
2(sin x)(cos x)
1
(sec x)^2
(csc x)^2
sin 2x
2(sin x)(cos x)
(sin x)^2 + (cos x)^2
1
22 terms
AB Calculus
Average Rate of Change/Average Velocity
Instantaneous Rate of Change/ Instanta…
Horizontal Tangent line
Finding the time when the object hits…
Slope over an interval- use f(x) to make a table
Slope at an instant (Need derivative)
Slope is zero (f prime=0)
Means position is 0 so set s(t)=0 and solve
Average Rate of Change/Average Velocity
Slope over an interval- use f(x) to make a table
Instantaneous Rate of Change/ Instanta…
Slope at an instant (Need derivative)
19 terms
Calculus AB
Limit
Power rule
Chain rule
Product rule
The value that a function or sequence approaches as the input…
d/dx[x^n]=nx^(n-1)
f'(u) • u' or f'(g(u)) • g'(u) • u'
f'(x)g(x) + f(x)g'(x)
Limit
The value that a function or sequence approaches as the input…
Power rule
d/dx[x^n]=nx^(n-1)
20 terms
Calculus AB
critical point
point of inflection
derivative tan(x)
derivative csc(x)
derivative is 0 or undefined
concavity changes (2nd derivative changes signs)
sec^2(x)
-csc(x)cot(x)
critical point
derivative is 0 or undefined
point of inflection
concavity changes (2nd derivative changes signs)
28 terms
Calculus AB
derivative of sin(x)
derivative of cos(x)
derivative of tan(x)
derivative of cot(x)
cos(x)
-sin(x)
sec^2(x)
-csc^2(x)
derivative of sin(x)
cos(x)
derivative of cos(x)
-sin(x)
27 terms
Calculus AB
n<m
N>m
N=M
L'Hopital
horizontal asymptote is y=0
Horizontal asymptote is none
horizontal asymptote by diving by the leading coefficient
f'(x)/g'(x) when there is an indeterminate form
n<m
horizontal asymptote is y=0
N>m
Horizontal asymptote is none
23 terms
AP Calculus AB SUMNOCO
Write the notation for the limit of f(…
Write the notation for the limit of f(…
State the 3 conditions of continuity o…
List the 3 situations in which a limit…
1. f(c) is defined... 2. The limit of f(x) as x approaches c exi…
1. Unbounded behavior... 2. Differing left/right behavior... 3. Osc…
Write the notation for the limit of f(…
Write the notation for the limit of f(…
11 terms
Calculus AB
f(x) max/min
f(x) increasing
f(x) decreasing
f(x) inflection point
f'(x) = 0
f'(x) > 0
f'(x) < 0
f'(x) max/min
f(x) max/min
f'(x) = 0
f(x) increasing
f'(x) > 0
18 terms
Calculus AB
If f'(x)<0 what is true of f(x)?
If f'(x)>0 what is true of f(x)?
Explain how to determine the critical…
If f'(x) is increasing what is true of…
f(x) is decreasing
f(x) is increasing
f'(x)=0 or when f'(x) is undefined
f(x) is concave up
If f'(x)<0 what is true of f(x)?
f(x) is decreasing
If f'(x)>0 what is true of f(x)?
f(x) is increasing
12 terms
AB calculus
y=cscx
y=cotx
y=3^x
y=arcsinx
-cscxcotx
-(cscx)^2
ln3•3^x
1/(1-x^2)^.5
y=cscx
-cscxcotx
y=cotx
-(cscx)^2
64 terms
AP Calculus AB Review
Find the zeros of f(x).
Find the intersection of f(x) and g(x).
Show that f(x) is even.
Show that f(x) is odd.
Set the function equal to 0. Factor or use quadratic formula…
Set the two functions equal to each other and solve.... Alternat…
Show that f(-x) = f(x). This shows that the graph of f is sym…
Show that f(-x) = -f(x). This shows that the graph of f is sy…
Find the zeros of f(x).
Set the function equal to 0. Factor or use quadratic formula…
Find the intersection of f(x) and g(x).
Set the two functions equal to each other and solve.... Alternat…
20 terms
Calculus AB AP - Limit Practice
10
5
6
3/2
Evaluate the limit in Part A given the following information:
Evaluate the limit in Part B given the following information:
Evaluate the limit in Part C given the following information:
Evaluate the limit in Part D given the following information:
10
Evaluate the limit in Part A given the following information:
5
Evaluate the limit in Part B given the following information:
69 terms
AP Calculus AB
1
0
Squeeze Theorem
f is continuous at x=c if...
1
0
87 terms
AP Calculus AB Knowledge
What conditions must be to satisfied f…
If the appropriate conditions are sati…
Limit
Quotient rule?
f(x) is continuous in the interval [a, b] and differentiable…
There is at least one point c in the interval (a, b) at which…
A limit is the value that a function or sequence "approaches"…
(vu'-uv')/v^2
What conditions must be to satisfied f…
f(x) is continuous in the interval [a, b] and differentiable…
If the appropriate conditions are sati…
There is at least one point c in the interval (a, b) at which…
73 terms
AP Calculus AB Vocab
absolute minimum
absolute maximim
absolute value
acceleration
The lowest point of a function.
The highest point of a function.
The distance between a number and the origin.
The rate of change of velocity over time.
absolute minimum
The lowest point of a function.
absolute maximim
The highest point of a function.
64 terms
AP Calculus AB Formulas
Definition of Derivative
Alternate Definition of Derivative
Volume using Disks
Volume using Washers
Definition of Derivative
Alternate Definition of Derivative
6 terms
AB Calculus
d/dx(tanx)
d/dx(sec(X))
d/dx(cos(x))
d/dx(cot(x))
sec^2(X)
tan(x)sec(x)
-sin(x)
-csc^2(x)
d/dx(tanx)
sec^2(X)
d/dx(sec(X))
tan(x)sec(x)
15 terms
AB Calculus: Derivatives
d/dx sinx = ... d/dx cosx = ... d/dx tanx =
d/dx arctanx =
d/dx arcsinx =
d/dx e^x = ... d/dx lnx =
d/dx sinx = ... d/dx cosx = ... d/dx tanx =
d/dx arctanx =
5 terms
Calculus AB
d/dx(xⁿ)
d/dx(sin x)
d/dx(cos x)
d/dx(tan x)
nxⁿ⁻¹
cos x
-sin x
sec²x
d/dx(xⁿ)
nxⁿ⁻¹
d/dx(sin x)
cos x
11 terms
AP Calculus AB Theorems
ƒ(x) ≤ g(x) ≤ h(x) for all x and if th…
If ƒ is continuous on [a,b] and k is a…
If ƒ(x) is continuous on [a,b], then ƒ…
The absolue extrema of a function cont…
Squeeze Theorem
Intermediate Value Theorem
Extreme Value Theorem
Absolute Extrema Theorem
ƒ(x) ≤ g(x) ≤ h(x) for all x and if th…
Squeeze Theorem
If ƒ is continuous on [a,b] and k is a…
Intermediate Value Theorem
14 terms
Tully - Calculus Theorems (AP Calculus AB/BC)
Intermediate Value Theorem
If f is continuous on [a,b] and k is b…
Rolle's Theorem
If f is continuous on [a,b] and f is d…
If f is continuous on [a,b] and k is between f(a) and f(b), t…
there is a number c in [a,b] such that f(c)=k.... (Intermediate…
If f is continuous on [a,b] and f is differentiable on (a,b)…
there is at least one number c in (a,b) such that f'(c)=0.... (…
Intermediate Value Theorem
If f is continuous on [a,b] and k is between f(a) and f(b), t…
If f is continuous on [a,b] and k is b…
there is a number c in [a,b] such that f(c)=k.... (Intermediate…
18 terms
AP Calculus AB Formulas
d/dx[sin(x)]
d/dx[cos(x)]
d/dx[tan(x)]
d/dx[sec(x)]
cos(x)
-sin(x)
sec^2(x)
sec(x)tan(x)
d/dx[sin(x)]
cos(x)
d/dx[cos(x)]
-sin(x)
64 terms
AP Calculus AB Formulas
Definition of Derivative
Alternate Definition of Derivative
Volume using Disks
Volume using Washers
Definition of Derivative
Alternate Definition of Derivative
8 terms
Calculus AB
Continuity
Limit does not exist (DNE) if
lim as x→0 (sin(x)/x)=
lim as x→[(1-cosx)/x]=
f(c) exists... lim as x→c of f(x) exists... f(c) =lim as x→c of f(x)
Left and right are not qual
1
0
Continuity
f(c) exists... lim as x→c of f(x) exists... f(c) =lim as x→c of f(x)
Limit does not exist (DNE) if
Left and right are not qual
25 terms
Derivatives for AP Calculus AB
d/dx(c) such that c is a constant
d/dx(cu) such that c is a constant
d/dx(u ± v)
d/dx(xⁿ)
0
cu'
u' ± v'
(nuⁿ⁻¹)u'
d/dx(c) such that c is a constant
0
d/dx(cu) such that c is a constant
cu'
63 terms
AP Calculus AB Exam
Intermediate Value Theorem
Average Rate of Change
Instantenous Rate of Change
Formal definition of derivative
If f(1)=-4 and f(6)=9, then there must be a x-value between 1…
Slope of secant line between two points, use to estimate inst…
Slope of tangent line at a point, value of derivative at a po…
limit as h approaches 0 of [f(a+h)-f(a)]/h
Intermediate Value Theorem
If f(1)=-4 and f(6)=9, then there must be a x-value between 1…
Average Rate of Change
Slope of secant line between two points, use to estimate inst…
27 terms
AP Calculus AB
2nd derivative is zero
f '' is negative
critical #'s occur when f '
f '' is positive
point of inflection
concave down, relative max
equals zero
concave up, relative minimum
2nd derivative is zero
point of inflection
f '' is negative
concave down, relative max
9 terms
Calculus AB
f(x)=xⁿ
f(x)= sin x
f(x)= cos x
f(x)= tan x
f'(x)=nxⁿ⁻¹
f'(x)= cos x
f'(x)= -sin x
f'(x)= sec² x
f(x)=xⁿ
f'(x)=nxⁿ⁻¹
f(x)= sin x
f'(x)= cos x
73 terms
AP Calculus AB Vocab
absolute minimum
absolute maximim
absolute value
acceleration
The lowest point of a function.
The highest point of a function.
The distance between a number and the origin.
The rate of change of velocity over time.
absolute minimum
The lowest point of a function.
absolute maximim
The highest point of a function.
148 terms
Calculus AB AP Exam
Critical Point
Inflection Point
Average Rate of Change
Volume by Washers
Possible Critical Point: where f '(x) is 0 OR UNDEFINED ... Indi…
Possible Inflection Point: where f"(x) is 0 OR UNDEFINED... Indi…
Critical Point
Possible Critical Point: where f '(x) is 0 OR UNDEFINED ... Indi…
Inflection Point
Possible Inflection Point: where f"(x) is 0 OR UNDEFINED... Indi…
39 terms
AP CALCULUS AB
Trig Identities
dy/dx
Intermediate Value Theorem
Extreme Value Theorem
There must be a max and min if the function is continuous on…
Trig Identities
dy/dx
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