Study sets matching "calculus b"

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Study sets matching "calculus b"

32 terms
Calculus B
Sequence
A sequence converges when
P-series
Geometric Series
a list of numbers written in a definite order
Sequence
a list of numbers written in a definite order
A sequence converges when
70 terms
calculus a/b review
f(x) increases when
derivative of secx
the limit exists if
Displacement
f'(x) is positive
secxtanx
the same value is approached from left and right
f(x)
f(x) increases when
f'(x) is positive
derivative of secx
secxtanx
45 terms
AP-B Calculus
Piecewise Function
Volume of a sphere
Horizontal Line Test
Vertical Line Test
Ex. y ={-3x - .5, -1 < x < 1 ; 2x + 1, 1 <= x <= 3
4/3 r^3 PI
A test to see if a horizontal line passes through the graph m…
A test use to determine if a relation is a function. A relati…
Piecewise Function
Ex. y ={-3x - .5, -1 < x < 1 ; 2x + 1, 1 <= x <= 3
Volume of a sphere
4/3 r^3 PI
Calculus B Formula
Hooke's Law
Work
Variable Force
Disks
F=kx
W=Fd
W=b∫a[F(x)]dx
∫[πr^2]dx
Hooke's Law
F=kx
Work
W=Fd
17 terms
Calculus A/B
tan(A)
cot(A)
sin^2(A) + cos^2(A)
tan^2(A) + 1
sin(A) / cos(A)
cos(A) / sin(A)
1
sec^2(A)
tan(A)
sin(A) / cos(A)
cot(A)
cos(A) / sin(A)
6 terms
Calculus B: Simple Derivatives
d/dx sinx
d/dx cosx
d/dx tanx
d/dx cotx
cosx
-sinx
sec^2 x
csc^2 x
d/dx sinx
cosx
d/dx cosx
-sinx
19 terms
calculus b exam 2
cos x
-sin x
sec^2 x
-csc x cot x
d/dx sin x
d/dx cos x
d/dx tan x
d/dx csc x
cos x
d/dx sin x
-sin x
d/dx cos x
17 terms
Calculus A/B
(xⁿ)'
[k×f(x)]'
(f×g)' wrong one
(b^x)'
nxⁿ⁻¹
k×f'(x)
f'×g' wrong one
b^x(lnb)
(xⁿ)'
nxⁿ⁻¹
[k×f(x)]'
k×f'(x)
Calculus A/B Study Set
Quotient rule:
Product Rule:
Chain Rule:
Derivative of Sin(x)
(gf'-fg')/g^2
Gf'+fg'
Work from the inside out
Cos(x)
Quotient rule:
(gf'-fg')/g^2
Product Rule:
Gf'+fg'
Chapter 4 Formulas Calculus A/B
cosx =
sinx =
sec^2x =
secxtanx =
sinx + c
-cosx + c
tanx + c
secx + c
cosx =
sinx + c
sinx =
-cosx + c
Calculus B Integrals/Derivatives/Identities
d/dx arcsinx
d/dx arccosx
d/dx arctanx
d/dx arccotx
1/√(1-x^2)
-1/√(1-x^2)
1/√(1+x^2)
-1/√(1+x^2)
d/dx arcsinx
1/√(1-x^2)
d/dx arccosx
-1/√(1-x^2)
AP Calculus A/B: Particle Motion
Initially
At rest
Particle moving right (forward or up)
Particle moving left (backward or down)
t=0
v(t)=0
v(t)>0
v(t)<0
Initially
t=0
At rest
v(t)=0
AP Calculus B/C: Big Theorems
IVT (Intermediate Value Theorem)
MVT (Mean Value Theorem)
EVT (Extreme Value Theorem)
AVT (Average Value Theorem)
On a continuous function you will hit every y-value between 2…
If conditions are met, there is at least one point where the…
Every continuous function on a closed interval has a highest…
If f(x) is integratable on [a,b] its average (mean) value on…
IVT (Intermediate Value Theorem)
On a continuous function you will hit every y-value between 2…
MVT (Mean Value Theorem)
If conditions are met, there is at least one point where the…
16 terms
BC Calculus Memory Quiz B
Definition of Continuity
Intermediate Value Theorem
Definition of Derivative
Alt. Form of Derivative
lim f(x) x->c f(x) = f(c)
1. If f is continuous [a,b] 2. and f(a) < k < f(b) or f(b) <…
f'(x) = lim h-> 0 f(x+h) - f(x) / h
f'(x) = lim x-> c f(x) - f(c) / x-c
Definition of Continuity
lim f(x) x->c f(x) = f(c)
Intermediate Value Theorem
1. If f is continuous [a,b] 2. and f(a) < k < f(b) or f(b) <…
30 terms
AP Calculus B/C Formulas & Stuff
derivative xⁿ
derivative sin x
derivative tan x
derivative cos x
nxⁿ⁻¹
cos x
sec²x
-sin x
derivative xⁿ
nxⁿ⁻¹
derivative sin x
cos x
48 terms
AP Calculus A/B Chapter 3
Corner
Vertical tangents
Cusp
Discontinuity
Piece wise and absolute value functions
_... 1/odd or odd\| Infinity on both sides
Even/odd power<1 one side +infinity one side -infinity
0 in denominator
Corner
Piece wise and absolute value functions
Vertical tangents
_... 1/odd or odd\| Infinity on both sides
24 terms
AP Calculus A/B Derivative Formulas
sin(x)]'
cos(X)]'
tan(x)]'
cot(x)]'
cos(x)
-sin(x)
sec^2(x)
-csc^2(x)
sin(x)]'
cos(x)
cos(X)]'
-sin(x)
AP Calculus B/C: PARTING the C
p-Series
Alternating Series
Root Test
Ratio Test
p-Series
Alternating Series
13 terms
Series/Sequences Flashcards (Calculus B/C)
Telescoping series
Harmonic series
Geometric series
Integral test
1/(n * (n+1))... -converges at 1
1 + 1/2 + 1/3 + 1/4 +...... -diverges
a + ar + ar^2 + ar^3 +...... -converges with sum S = a/(1 - r) I…
series E(an) where f(n) = an and f(x) is when x replaces n. I…
Telescoping series
1/(n * (n+1))... -converges at 1
Harmonic series
1 + 1/2 + 1/3 + 1/4 +...... -diverges
8 terms
Joshua - Calculus A/B Test #1 Notes
Odd Function
Even Function
Symmetrical to X Axis
Symmetrical to Y axis
f(-x) = -f(x)
f(x) = f(-x)
Substitute y with -y and get the same function
Substitute x with -x and get the same function
Odd Function
f(-x) = -f(x)
Even Function
f(x) = f(-x)
Pre-Calculus b: Chapter 10 Identities
sin(α+β)
sin(α-β)
cos(α+β)
cos(α-β)
sinαcosβ+cosαsinβ
sinαcosβ-cosαsinβ
cosαcosβ-sinαsinβ
cosαcosβ+sinαsinβ
sin(α+β)
sinαcosβ+cosαsinβ
sin(α-β)
sinαcosβ-cosαsinβ
72 terms
A. P. Calculus B. C. Midterm Formulas Review
Polar identity of x
Polar identity of y
Rectangular identity of r
Polar Area
x = rcosθ
y = rsinθ
r² = x² + y²
A = a∫b 1/2(r²)dθ
Polar identity of x
x = rcosθ
Polar identity of y
y = rsinθ
13 terms
Calculus A/B Chapter 2.1-2.3
d/dx (cosx)
d/dx (sinx)
d/dx (tanx)
d/dx (cotx)
-sinx
cosx
sec^2x
-csc^2x
d/dx (cosx)
-sinx
d/dx (sinx)
cosx
Mrs. Bonn Chapter 9 flash cards AP Calculus B/C
Infinite Series
Infinite Series (sequence of partial s…
Convergence of an Infinite Series
Geometric Series
Sn =a1+a2+a3....+an
S1 =a1 ... S2= a1+ a2... Sn = a1+a2+....+an
In inifinite series converges to S if lin Sn as N approaches…
a + ar + ar^2 = ar^3 +....> + ar^n-1 + ....
Infinite Series
Sn =a1+a2+a3....+an
Infinite Series (sequence of partial s…
S1 =a1 ... S2= a1+ a2... Sn = a1+a2+....+an
9 terms
Calculus a/b Sec. 2.3-2.4
product rule
quotient rule
f(x) = tanx
f(x)=cscx
f(x)*g'(x)+g(x)*f'(x)
g(x)*f'(x)-f(x)*g'(x)/[g(x)]^2
f'(x) = sec^2x
f'(x)= -cscxcotx
product rule
f(x)*g'(x)+g(x)*f'(x)
quotient rule
g(x)*f'(x)-f(x)*g'(x)/[g(x)]^2
12 terms
CALCULUS
Two Special Trigonometric Limits
Definition of the Derivative of a Func…
Average Velocity or Average rate of Ch…
Properties of the Natural Logarithmic…
limx-->0 (sinx) / x = 1... lim x-->0 (1-cosx) / x = 0
f ' (x) = lim Δx-->0 [f(x+Δ x) - f(x)] / Δx
[f(b) - f(a)] / (b - a)
a. The domain is (0, ∝) and the range is (-∝,∝)... b. ln(1) = 0…
Two Special Trigonometric Limits
limx-->0 (sinx) / x = 1... lim x-->0 (1-cosx) / x = 0
Definition of the Derivative of a Func…
f ' (x) = lim Δx-->0 [f(x+Δ x) - f(x)] / Δx
54 terms
Calculus
sin²x + cos²x
1 + tan²x
1 + cot²x
sin(-x)
1
sec²x
csc²x
-sin x
sin²x + cos²x
1
1 + tan²x
sec²x
65 terms
Pre-Calculus
Function
Relation
Domain
Range
A relationship from one set (called the domain) to another se…
An association between two or more variables. If one of the v…
All of the input or x values in a function
All of the output or y values in a function
Function
A relationship from one set (called the domain) to another se…
Relation
An association between two or more variables. If one of the v…
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)=
AP Calculus AB Formulas
Definition of Derivative
Alternate Definition of Derivative
Volume using Disks
Volume using Washers
Definition of Derivative
Alternate Definition of Derivative
75 terms
AP Calculus Flash Cards_AB
1
0
Squeeze Theorem
f is continuous at x=c if...
1
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:
54 terms
Calculus
sin²x + cos²x
1 + tan²x
1 + cot²x
sin(-x)
1
sec²x
csc²x
-sin x
sin²x + cos²x
1
1 + tan²x
sec²x
36 terms
PreCalculus: Vocabulary Algebra Review
Complex Fraction
Compound Inequality
Cube root
Distance Formula
A fraction that contains one or more fractions in its numerat…
Two or more inequalities joined together by "and" or "or"
a number that when multiplied three times equals a given number
d = √[( x₂ - x₁)² + (y₂ - y₁)²]
Complex Fraction
A fraction that contains one or more fractions in its numerat…
Compound Inequality
Two or more inequalities joined together by "and" or "or"
56 terms
Calculus
sin²x + cos²x
1 + tan²x
1 + cot²x
sin(-x)
1
sec²x
csc²x
-sin x
sin²x + cos²x
1
1 + tan²x
sec²x
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:
CALCULUS
Two Special Trigonometric Limits
Definition of the Derivative of a Func…
Average Velocity or Average rate of Ch…
Guidelines for Implicit Differentiation
limx-->0 (sinx) / x = 1... lim x-->0 (1-cosx) / x = 0
f ' (x) = lim Δx-->0 [f(x+Δ x) - f(x)] / Δx
[f(b) - f(a)] / (b - a)
a. Differentiate both sides of the equation with respect to x…
Two Special Trigonometric Limits
limx-->0 (sinx) / x = 1... lim x-->0 (1-cosx) / x = 0
Definition of the Derivative of a Func…
f ' (x) = lim Δx-->0 [f(x+Δ x) - f(x)] / Δx
21 terms
Calculus Formulas
a^2+b^2=c2
A=(pi)r^2
A=lw
V=s^3
Pythagorean Theorem
Area of Circle
Area of Rectangle
Volume of Cube
a^2+b^2=c2
Pythagorean Theorem
A=(pi)r^2
Area of Circle
16 terms
Calculus A Formulas and Theorems
Definition of a limit using derivatives
Intermediate Value Theorem (IVT)
Horizontal Asymptote
Vertical Asymptote
Definition of a limit using derivatives
Intermediate Value Theorem (IVT)
Calculus
sin²x + cos²x
1 + tan²x
1 + cot²x
sin(-x)
1
sec²x
csc²x
-sin x
sin²x + cos²x
1
1 + tan²x
sec²x
Pre calculus
Fundamental Theorem of Algebra
Complex Zeros Occur in Conjugate Pairs
Logarithmic Functions
Natural Logarithmic Functions
1.A polynomial of degree n, where n>o, has exactly n roots in…
1.If a + bi, where b does not equal 0, is a zero of the funct…
1.For x>0, a>0, and a can't equal 1, y=log of x with base a i…
1.For X>0, y=lnx if and only if X=e to the y power.... 2.The fun…
Fundamental Theorem of Algebra
1.A polynomial of degree n, where n>o, has exactly n roots in…
Complex Zeros Occur in Conjugate Pairs
1.If a + bi, where b does not equal 0, is a zero of the funct…
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)
33 terms
Calculus
State the Intermediate Value Theorem
State the Chain Rule for Differentiation
What is the integral of ln(x)?
What is the Product Rule?
If the function f(x) is continuous on [a,b], and y is a numbe…
n(f(x))^n-1 * f'(x)
...
[f(x) g'(x)] + [f('x) g(x)]
State the Intermediate Value Theorem
If the function f(x) is continuous on [a,b], and y is a numbe…
State the Chain Rule for Differentiation
n(f(x))^n-1 * f'(x)
15 terms
Calculus Identities
tan(x)
cot(x)
sec(x)
csc(x)
sin(x)/cos(x)
cos(x)/sin(x)
1/cos(x)
1/sin(x)
tan(x)
sin(x)/cos(x)
cot(x)
cos(x)/sin(x)
19 terms
Calculus Identities
Dx(Sinx)
Dx(Cosx)
Dx(Tanx)
Dx(Cotx)
Cosx
-Sinx
Sec^2x derivative
-Csc^2x
Dx(Sinx)
Cosx
Dx(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
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
20 terms
Pre-Calculus Chapter 1
Slope
Point slope form
Slope intercept
General form
m = rise/run = y2 - y1/x2-X1
(y-y1) = m(x-x1)
y = mx + b
0 = Ax + Bx + C
Slope
m = rise/run = y2 - y1/x2-X1
Point slope form
(y-y1) = m(x-x1)
Calc B
LIPET
A in polar graph
A between polar graphs
Dy/dt=ky(m-y)
Logs inversetrig poly exponents trig
.5 integral r^2d0
.5 integral R^2-r^2d0
Y=Ce^(kt)
LIPET
Logs inversetrig poly exponents trig
A in polar graph
.5 integral r^2d0
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