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Study sets matching "calculus ab"

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
62 terms
Calculus AB
1
0
Squeeze Theorem
f is continuous at x=c if...
1
0
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
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,
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
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
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
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…
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
36 terms
AB Calculus
When asked to INTERPRET
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
When asked to INTERPRET
state when, what, how, and how much
Numerical derivative on calculator por…
does not require work to be shown
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:
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…
69 terms
AP Calculus AB
1
0
Squeeze Theorem
f is continuous at x=c if...
1
0
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 =
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'
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(…
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
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
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
251 terms
Calculus AB
Given f(x)=√(x+3)-2, sketch graph and…
Find the domain of the function: h(x)=…
Given the piecewise function:... f(x)= (-…
D=[-3,∞)... R=[-2,∞)
need help
D=(-∞,∞)... R= (-4,∞)
Given f(x)=√(x+3)-2, sketch graph and…
D=[-3,∞)... R=[-2,∞)
Find the domain of the function: h(x)=…
need help
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)
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…
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)
50 terms
Calculus ab
X ccu
X' incr
X'' >0
Area of a circle
X' incr, x''>0
X ccu, x''>0
X ccu, x' incr
A=pi.r^2
X ccu
X' incr, x''>0
X' incr
X ccu, x''>0
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
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:
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)
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)
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
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
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
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
84 terms
Calculus AB Flashcards
Vertical Asymptote
Point Slope Form
lim (1-cosx)/x... x-->0
lim sinx/x... x-->0
Vertical asymptotes are vertical lines which correspond to th…
=0
=1
Vertical Asymptote
Vertical asymptotes are vertical lines which correspond to th…
Point Slope Form
45 terms
Chapter 3 Calculus AB
definition of a derivitive
definition of a derivative (alternative)
the derivative does not exist at
difference quotient
Lim h->0 (f(x+h)-f(x)) ÷ (x+h-x)
Lim x->a (f(x)-f(a))÷ (x-a)
corner, cusp, vertical tangent
(f(a+h)-f(a))÷ h
definition of a derivitive
Lim h->0 (f(x+h)-f(x)) ÷ (x+h-x)
definition of a derivative (alternative)
Lim x->a (f(x)-f(a))÷ (x-a)
65 terms
AP Calculus AB 2
Definition of Derivative
Alternate Definition of Derivative
Volume using Disks
Volume using Washers
Definition of Derivative
Alternate Definition of Derivative
13 terms
AP Calculus AB - Derivatives
cos x
-sin x
sec2 x
sec x tan x
d/dx sin x
d/dx cos x
d/dx tan x
d/dx sec x
cos x
d/dx sin x
-sin x
d/dx cos x
13 terms
AP Calculus AB - Integrals
-cos x + c
sin x + c
tan x + c
-cot x + c
∫ sin x dx
∫ cos x dx
∫ sec2 x dx
∫ csc2 x dx
-cos x + c
∫ sin x dx
sin x + c
∫ cos x dx
69 terms
AP Calculus AB 1
1
0
Squeeze Theorem
f is continuous at x=c if...
1
0
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…
69 terms
AP Calculus AB
1
0
Squeeze Theorem
f is continuous at x=c if...
1
0
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)
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…
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
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
56 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
69 terms
AP Calculus AB
1
0
Squeeze Theorem
f is continuous at x=c if...
1
0
39 terms
AP CALCULUS AB
Find the Zeros
Find the equation of the line tangent…
Find the interval where f(x) is increa…
Find the interval where the slope of f…
f(x)=0
Find a point (x, y) and the slope (using the derivative) then…
f'(x) is positive
f''(x) is positive
Find the Zeros
f(x)=0
Find the equation of the line tangent…
Find a point (x, y) and the slope (using the derivative) then…
56 terms
Calculus AB Theorems
Theorem 1.1: Some Basic Limit
Theorem 1.2: Properties of Limits
Theorem 1.3: Limits of Polynomial and…
Theorem 1.4: The Limit of a Function I…
Theorem 1.1: Some Basic Limit
Theorem 1.2: Properties of Limits
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