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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)
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)
11 terms
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'
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)
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
10 terms
AP Calculus B/C: PARTING the C
p-Series
Alternating Series
Root Test
Ratio Test
p-Series
Alternating Series
16 terms
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
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
16 terms
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
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)
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
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
28 terms
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
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 AB Formulas
Definition of Derivative
Alternate Definition of Derivative
Volume using Disks
Volume using Washers
Definition of Derivative
Alternate Definition of Derivative
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
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)
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…
54 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:
75 terms
AP Calculus Flash Cards_AB
1
0
Squeeze Theorem
f is continuous at x=c if...
1
0
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"
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:
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
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
63 terms
Calc. Vocab.
slope
domain
function
point-slope equation
(y₂-y₁)/(x₂-x₁)
x-values, watch for fractions (denom.≠0)... and square roots ("s…
each x has exactly one y... passes vertical line test
y-y₁=m(x-x₁)
slope
(y₂-y₁)/(x₂-x₁)
domain
x-values, watch for fractions (denom.≠0)... and square roots ("s…
69 terms
AP Calculus AB
1
0
Squeeze Theorem
f is continuous at x=c if...
1
0
23 terms
Calculus AB AP - 1.2 -1.3 Quiz Review
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:
145 terms
AP Calculus AB Cumulative Chapter Terms
a/b > 0 when
| a | = b when
| a | > b when
| a | < b when
signs of a and b are the same
a = b or -a = b
a > b or a < -b
-b < a < b
a/b > 0 when
signs of a and b are the same
| a | = b when
a = b or -a = b
54 terms
Calculus
sin²x + cos²x
1 + tan²x
1 + cot²x
sin(-x)
1
sec²x
csc²x
-sin x
sin²x + cos²x
1
1 + tan²x
sec²x
54 terms
Calculus
sin²x + cos²x
1 + tan²x
1 + cot²x
sin(-x)
1
sec²x
csc²x
-sin x
sin²x + cos²x
1
1 + tan²x
sec²x
20 terms
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…
21 terms
Differential Calculus Terms
Derivative of a function at a point
Mean Value Theorem
Critical point of a function
Local minimum
Limit of the slopes of secant lines to provide the slope of t…
Slope of secant joining the endpoints of an interval from a t…
A number in the domain of f where either the derivative equal…
Local minimum occurs at a critical point where the sign of th…
Derivative of a function at a point
Limit of the slopes of secant lines to provide the slope of t…
Mean Value Theorem
Slope of secant joining the endpoints of an interval from a t…
65 terms
Pre-Calculus Terms
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…
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
120 terms
"When you see this, think this..."-- AP Calculus
Find the zeros
show that f(x) is even
show that f(x) is odd
show that lim(x→a) of f(x) exists
Find roots... set function=0... factor or use quad equation... graph t…
show that f(-x)=f(x)... symmetric to y axis
show that f(-x)= -f(x) OR f(x)= -f(-x)... symmetric around origin
show that lim(x→a⁻) f(x)= lim (x→a⁺) f(x) exists and are equal
Find the zeros
Find roots... set function=0... factor or use quad equation... graph t…
show that f(x) is even
show that f(-x)=f(x)... symmetric to y axis
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…
26 terms
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
56 terms
Calculus
sin²x + cos²x
1 + tan²x
1 + cot²x
sin(-x)
1
sec²x
csc²x
-sin x
sin²x + cos²x
1
1 + tan²x
sec²x
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)
128 terms
Sharise's Calculus vocab
linear equation, three forms- what are…
slope-intercept form:
point-slope form:
standard form:
slope-intercept form, point-slope form, and standard form
y = mx + b
y-y₁=m(x-x₁)
Ax + By = C
linear equation, three forms- what are…
slope-intercept form, point-slope form, and standard form
slope-intercept form:
y = mx + b
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