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#### Study sets matching "ap calculus"

10 terms
AP CALCULUS
Derivative
Implicit differentiation
tangent
Secant
A function which gives the slope of a curve; that is, the slo…
The process of finding the derivative of a dependent variable…
A straight line or plane that touches a curve or curved surfa…
A secant is a line that intersects a circle at two points.
Derivative
A function which gives the slope of a curve; that is, the slo…
Implicit differentiation
The process of finding the derivative of a dependent variable…
28 terms
AP Calculus
Trig Derivatives
Solids of Revolution
Solids of Known Cross Section
Integrals as Net Change
V=∫(from a to b) A(x)dx... A(x)=πr²... 1. Sketch the region... 2. Dete…
v=∫(from a to b) A(x)dx... 1. Sketch the region and a cross sect…
∫(from a to b) v(t)dt = Displacement, give the net change in…
Trig Derivatives
Solids of Revolution
V=∫(from a to b) A(x)dx... A(x)=πr²... 1. Sketch the region... 2. Dete…
69 terms
AP Calculus
related rates
taylor polynomials
sinx
cosx
take the equation they give you and derive and solve with the…
cosx
-sinx
related rates
taylor polynomials
take the equation they give you and derive and solve with the…
9 terms
AP Calculus 1- Limits
End behavior
Exponential Decay
Exponential Growth
Limit
The appearance of a graph as it is followed farther and farth…
A model for decay of a quantity for which the rate of decay i…
This model is used for such phenomena as inflation or populat…
The value that a function or expression approaches as the dom…
End behavior
The appearance of a graph as it is followed farther and farth…
Exponential Decay
A model for decay of a quantity for which the rate of decay i…
75 terms
AP Calculus Flash Cards
1
0
Squeeze Theorem
f is continuous at x=c if...
1
0
47 terms
Key Terms For AP Calculus
Natural Numbers
Integers
Whole Numbers
Rational Numbers
The set of numbers 1, 2, 3, 4, ... Also called counting numbe…
The set of whole numbers and their opposites
Natural numbers ( counting numbers) and zero; 0, 1, 2, 3...
The set of any numbers that can be expressed as a fraction
Natural Numbers
The set of numbers 1, 2, 3, 4, ... Also called counting numbe…
Integers
The set of whole numbers and their opposites
28 terms
AP Calculus
IVT
EVT
MVT
Rolles Theorum
If a function is continuous on [a,b], then it passes through…
If f is continuous over a closed interval, then f has a max a…
if f is continuous on [a,b] and differentiable, the instant r…
If f is continuous on [a,b] and diff, there must be a max and…
IVT
If a function is continuous on [a,b], then it passes through…
EVT
If f is continuous over a closed interval, then f has a max a…
17 terms
AP Calculus
Normal Line
Normal Slope
Tangent Line
Secant Line
Perpindicular to tangent line.
The derivative of f(x) at the point a1 then finding the negat…
...
...
Normal Line
Perpindicular to tangent line.
Normal Slope
The derivative of f(x) at the point a1 then finding the negat…
27 terms
AP Calculus
d/dx (sin u)
d/dx (cos u)
d/dx (csc u)
d/dx (sec u)
(cos u)u'
-(sin u)u'
-(csc u cot u)u'
(sec u tan u)u'
d/dx (sin u)
(cos u)u'
d/dx (cos u)
-(sin u)u'
176 terms
Calculus Review For AP Exam
1
0
Squeeze Theorem
f is continuous at x=c if...
1
0
20 terms
AP Calculus
d/dx (x^2)
d/dx (sin x)
d/dx (cos x)
d/dx (tan x)
2x
cos x
-sin x
(sec x)^2
d/dx (x^2)
2x
d/dx (sin x)
cos x
64 terms
AP Calculus Review - Pre-calculus Topics
Area of a Triangle
Area of a Triangle (SAS Formula)
Area of a Trapezoid
Area of a Circle
Area of a Triangle
Area of a Triangle (SAS Formula)
6 terms
AP Calculus/Calculus Review
rolle's theorem
mean value theorem
extrema
critical values
1) check that you can use rolle's theorem... -is it continuous?…
f(x) has to be continuous and differentiable... defined over [a,…
extrema = relative min or max... derivative of the function = 0…
-relative min/max only occur at cv... cv are f'(c) = 0 or f'(c)…
rolle's theorem
1) check that you can use rolle's theorem... -is it continuous?…
mean value theorem
f(x) has to be continuous and differentiable... defined over [a,…
75 terms
AP Calculus Flash Cards_AB
1
0
Squeeze Theorem
f is continuous at x=c if...
1
0
100 terms
AP Calculus
Area of a Right Triangle
Sine (Sin)
Cosine (Cos)
Tangent (Tan)
(½)(Base)(Height)
Opposite/Hypotenuse
Area of a Right Triangle
(½)(Base)(Height)
Sine (Sin)
Opposite/Hypotenuse
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
32 terms
Kriegl AP Calculus derivatives
f'(x)
Alternate form of derivative ... f'(a)=
1
d/dx c
1
0
f'(x)
Alternate form of derivative ... f'(a)=
65 terms
AP Calculus Review - Differentiation
Definition of a Derivative f'(x)
Definition of a Derivative at a Point…
If f is differentiable at x=a ...
Rolle's Theorem
then f is continuous at x=a.
Definition of a Derivative f'(x)
Definition of a Derivative at a Point…
19 terms
AP Calculus Integrals
∫ a dx
∫ 1/x dx
∫ e^x ds
∫ a^x dx
ax + c
ln | x | + c
e^x + c
a^x/ ln a + c
∫ a dx
ax + c
∫ 1/x dx
ln | x | + c
20 terms
AP Calculus
Sinx
Cosx
Tanx
Cotx
1/Cscx
1/Secx
1/Cotx... Sinx/Cosx
Cosx/Sinx
Sinx
1/Cscx
Cosx
1/Secx
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
53 terms
AP Calculus
Derivative of sinx
Derivative of cosx
Derivative of tanx
Derivative of secx
cosx
-sinx
secx • secx
secx • tanx
Derivative of sinx
cosx
Derivative of cosx
-sinx
20 terms
Ap Calculus Angle Identities
sin²x + cos²x
1 + tan²x
1 + cot²x
sin(-x)
1
sec²x
csc²x
-sin x
sin²x + cos²x
1
1 + tan²x
sec²x
9 terms
AP Calculus General Stuff
Log A + Log B
Log A - Log B
k Log A
Point-slope form of a line
Log (AB)
Log (A/B)
Log (A^k)
y-y1 = m (x-x1)
Log A + Log B
Log (AB)
Log A - Log B
Log (A/B)
75 terms
AP Calculus Flash Cards
1
0
Squeeze Theorem
f is continuous at x=c if...
1
0
26 terms
AP Calculus Review - Integration
We use a Riemann Sum to approximate th…
= 0... Note the limits on the integral.
Note the limits on the integral. Use a…
f(x) must be continuous on [a, b]. The…
Riemann Sums
The "Zero" Integral
Order of Integration
Mean Value Theorem for Definite Integrals
We use a Riemann Sum to approximate th…
Riemann Sums
= 0... Note the limits on the integral.
The "Zero" Integral
75 terms
AP Calculus Flash Cards_AB
1
0
Squeeze Theorem
f is continuous at x=c if...
1
0
15 terms
AP Calculus Derivatives
d/dx (x^n)
d/dx (fg)
d/dx (f/g)
d/dx f(g(x))
nx^n - 1
fg' + gf'
(gf' - fg')/g²
f'(g(x))g'(x)
d/dx (x^n)
nx^n - 1
d/dx (fg)
fg' + gf'
75 terms
AP Calculus Flash Cards
1
0
Squeeze Theorem
f is continuous at x=c if...
1
0
67 terms
AP Calculus
Double angle identity for sin^2θ
cos^2θ+sin^2θ
1/(cosθ)
sin2θ
1/2(1-cos2θ)
1
secθ
2sinθcosθ
Double angle identity for sin^2θ
1/2(1-cos2θ)
cos^2θ+sin^2θ
1
75 terms
AP Calculus Flash Cards_AB
1
0
Squeeze Theorem
f is continuous at x=c if...
1
0
15 terms
AP Calculus
d/dx sin(x)
dy/dx sin⁡(x)
dy/dx cos⁡(x)
dy/dx tan⁡(x)
cos(x)
cos⁡(x)
-sin⁡(x)
sec^2 (x)
d/dx sin(x)
cos(x)
dy/dx sin⁡(x)
cos⁡(x)
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)
30 terms
AP Calculus 2- Understanding the Derivative
Derivative
Discontinuity
Increasing Function
Infinity
A function which gives the slope of a curve; that is, the slo…
A point at which the graph of a relation or function is not c…
A function with a graph that goes up as it is followed from l…
A "number" which indicates a quantity, size, or magnitude tha…
Derivative
A function which gives the slope of a curve; that is, the slo…
Discontinuity
A point at which the graph of a relation or function is not c…
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…
75 terms
AP Calculus Flash Cards_AB
1
0
Squeeze Theorem
f is continuous at x=c if...
1
0
21 terms
AP Calculus
d/dx (x^2)
d/dx (sin x)
d/dx (cos x)
d/dx (tan x)
2x
cos x
-sin x
(sec x)^2
d/dx (x^2)
2x
d/dx (sin x)
cos x
23 terms
AP Calculus
amplitude/period of f(x) = x sin bx
period of f(x) = tan cx
domain of inverse sin x
a^m * a^n =
Amplitude: A... Period 2pi/b
pi/c
...
a^(m+n)
amplitude/period of f(x) = x sin bx
Amplitude: A... Period 2pi/b
period of f(x) = tan cx
pi/c
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
16 terms
AP Calculus
Vertical Asymptote
Point-slope form
limits with trig functions
Intermediate Value Theorem
Y=mx+b
sin'2 +cos'2 = 1 Make sure when writing reasoning to show tha…
Vertical Asymptote
Point-slope form
Y=mx+b
29 terms
AP Calculus Review - Limits
1... In general, as x→0, sin(kx) → kx. S…
0
Does Not Exist
0
1... In general, as x→0, sin(kx) → kx. S…
0
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:
8 terms
AP Calculus Limits
Definition of a Limit
IVT (Intermediate Value Theorem)
Definition of continuity
definition of Vertical Asymptote
lim f(x) = lim f(x)... x->a- .... x->a+
if f(x) is continuous on [a,b], there exists a point "c" betw…
f(x) is continuous if and only if :... f(a) exists... lim f(x) exis…
x=a is a VA if and only if ... lim f(x) = ∞ or -∞... x->a
Definition of a Limit
lim f(x) = lim f(x)... x->a- .... x->a+
IVT (Intermediate Value Theorem)
if f(x) is continuous on [a,b], there exists a point "c" betw…
75 terms
AP Calculus Flash Cards_AB
one
zero
Squeeze Theorem
f is continuous at x=c if...
one
zero
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…
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:
57 terms
AP Calculus BC
Product rule Derivatives
Volume of Disc
Volume of Washer
Volume of Shell
Product rule Derivatives
Volume of Disc
96 terms
AP Calculus BC 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…
40 terms
AP Calculus Flash Cards
1
0
Squeeze Theorem
f is continuous at x=c if...
1
0
32 terms
AP Calculus Ch. 3 Derivatives
Cusp
Corner
vertical tangent line
discontinuity
Cusp
Corner
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