1
Q
What is the Logarithm Product Rule?
A
ln(ab) = ln(a) + ln(b)
2
Q
What is the Logarithm Quotient Rule?
A
ln(a/b) = ln(a) - ln(b)
3
Q
What is the Logarithm Power Rule?
A
ln(a^b) = b * ln(a)
4
Q
What is the Logarithm Change of Base Formula?
A
log_a(x) = ln(x) / ln(a)
5
Q
What is the Inverse Property of e and ln (e raised to ln)?
A
e^(ln x) = x
6
Q
What is the Inverse Property of ln and e (ln of e raised to)?
A
ln(e^x) = x
7
Q
What is the value of ln(1)?
A
0
8
Q
What is the value of ln(e)?
A
1
9
Q
What is the Exponent Multiplication Rule (x^a * x^b)?
A
x^(a+b)
10
Q
What is the Exponent Division Rule (x^a / x^b)?
A
x^(a-b)
11
Q
What is the Power of a Power Rule ((x^a)^b)?
A
x^(ab)
12
Q
What is the Negative Exponent Rule (x^-n)?
A
1 / (x^n)
13
Q
What is the Fractional Exponent Rule (x^(p/q))?
A
q-th root of (x^p) OR (q-th root of x)^p
14
Q
What is the algebraic definition of an Even Function?
A
f(-x) = f(x)
15
Q
What is the algebraic definition of an Odd Function?
A
f(-x) = -f(x)
16
Q
What is the geometric symmetry of an Even Function?
A
y-axis symmetry
17
Q
What is the geometric symmetry of an Odd Function?
A
Origin symmetry
18
Q
What is the Integral Property of an Even Function from -a to a?
A
2 * [Integral from 0 to a of f(x) dx]
19
Q
What is the Integral Property of an Odd Function from -a to a?
A
0
20
Q
What is the piecewise definition of the Absolute Value function |x|?
A
x if x >= 0; -x if x < 0
21
Q
What is the slope-intercept form of a line?
A
y = mx + b
22
Q
What is the point-slope form of a line (Leibniz-friendly)?
A
y - y1 = m(x - x1)
23
Q
What is the formula for the slope (m) between two points?
A
m = (y2 - y1) / (x2 - x1)
24
Q
What is the Quadratic Formula?
A
x = [-b ± sqrt(b^2 - 4ac)] / 2a
25
What is the Binomial Expansion of (a + b)^2?
a^2 + 2ab + b^2
26
What is the Binomial Expansion of (a - b)^2?
a^2 - 2ab + b^2
27
What is the Difference of Squares factorization?
a^2 - b^2 = (a - b)(a + b)
28
What is the Sum of Cubes factorization?
a^3 + b^3 = (a + b)(a^2 - ab + b^2)
29
What is the Difference of Cubes factorization?
a^3 - b^3 = (a - b)(a + b + b^2)
30
What is the quotient identity for tan(x)?
sin(x) / cos(x)
31
What is the quotient identity for cot(x)?
cos(x) / sin(x)
32
What is the reciprocal identity for sec(x)?
1 / cos(x)
33
What is the reciprocal identity for csc(x)?
1 / sin(x)
34
What is the fundamental Pythagorean identity?
sin^2(x) + cos^2(x) = 1
35
What is the Pythagorean identity involving tan(x)?
1 + tan^2(x) = sec^2(x)
36
What is the Pythagorean identity involving cot(x)?
1 + cot^2(x) = csc^2(x)
37
What is the double angle formula for sin(2x)?
2sin(x)cos(x)
38
What is the primary form of the double angle formula for cos(2x)?
cos^2(x) - sin^2(x)
39
What is the double angle formula for cos(2x) in terms of cosine only?
2cos^2(x) - 1
40
What is the double angle formula for cos(2x) in terms of sine only?
1 - 2sin^2(x)
41
What is the power reduction formula for sin^2(x)?
(1 - cos(2x)) / 2
42
What is the power reduction formula for cos^2(x)?
(1 + cos(2x)) / 2
43
What is the odd/even symmetry property for sin(-x)?
-sin(x) (Odd function)
44
What is the odd/even symmetry property for cos(-x)?
cos(x) (Even function)
45
What is the odd/even symmetry property for tan(-x)?
-tan(x) (Odd function)
46
What are the (cos, sin) coordinates and tan value for 0 radians?
(cos, sin) coordinates: (1, 0). tan value: 0
47
What are the (cos, sin) coordinates and tan value for pi/6 radians?
(cos, sin) coordinates: (sqrt(3)/2, 1/2). tan value: 1/sqrt(3)
48
What are the (cos, sin) coordinates and tan value for pi/4 radians?
(cos, sin) coordinates: (sqrt(2)/2, sqrt(2)/2). tan value: 1
49
What are the (cos, sin) coordinates and tan value for pi/3 radians?
(cos, sin) coordinates: (1/2, sqrt(3)/2). tan value: sqrt(3)
50
What are the (cos, sin) coordinates and tan value for pi/2 radians?
(cos, sin) coordinates: (0, 1). tan value: undefined
51
What is the period of the sine and cosine functions?
2*pi
52
What is the period of the tangent and cotangent functions?
pi
53
What are the criteria for the existence of a limit lim_{x -> c} f(x)?
The left-hand limit must equal the right-hand limit: lim{x -> c^-} f(x) = lim{x -> c^+} f(x) = L.
54
What are the three criteria for a function f(x) to be continuous at a point x = c?
1. f(c) is defined. 2. lim{x -> c} f(x) exists. 3. lim{x -> c} f(x) = f(c).
55
What is the definition of a Vertical Asymptote at x = a?
A vertical asymptote exists at x = a if lim{x -> a^-} f(x) = ±infinity or lim{x -> a^+} f(x) = ±infinity.
56
What is the definition of a Horizontal Asymptote at y = L?
A horizontal asymptote exists at y = L if lim{x -> infinity} f(x) = L or lim{x -> -infinity} f(x) = L.
57
What are the two indeterminate forms required to apply L'Hôpital's Rule?
The limit must produce the indeterminate form 0/0 or ±infinity/±infinity.
58
State L'Hôpital's Rule in both Lagrange and Leibniz notation.
Lagrange: lim{x -> c} [f(x)/g(x)] = lim{x -> c} [f'(x)/g'(x)]. Leibniz: lim{x -> c} [f(x)/g(x)] = lim{x -> c} [(d/dx f(x))/(d/dx g(x))].
59
What is the value of the special trigonometric limit lim_{x -> 0} [sin(x)/x]?
1
60
What is the value of the special trigonometric limit lim_{x -> 0} [(1 - cos(x))/x]?
0
61
What is the limit definition of the constant 'e'?
lim{x -> infinity} (1 + 1/x)^x = e or lim{x -> 0} (1 + x)^(1/x) = e.
62
What is the value of the special limit lim_{n -> infinity} [nth-root of n]?
1
63
State the conditions and result of the Squeeze (Sandwich) Theorem.
Conditions: g(x) <= f(x) <= h(x) near c and lim{x -> c} g(x) = lim{x -> c} h(x) = L. Result: lim_{x -> c} f(x) = L.
64
State the conditions and result of the Intermediate Value Theorem (IVT).
Condition: f(x) is continuous on the closed interval [a, b]. Result: For any value k between f(a) and f(b), there exists at least one c in [a, b] such that f(c) = k.
65
What is the theorem regarding Differentiability and Continuity?
Theorem: If f is differentiable at x = c, then f is continuous at x = c. (Note: The converse is FALSE; continuity does not guarantee differentiability).
66
What are the three common types of discontinuities?
1. Removable (Hole). 2. Jump (Step). 3. Infinite (Vertical Asymptote).
67
How do you remove a 'Removable Discontinuity' at x = c?
Redefine f(c) such that f(c) = lim_{x -> c} f(x).
68
What is the limit definition of the derivative (h-form) in Lagrange and Leibniz notation?
Lagrange: f'(x) = lim (h->0) [f(x+h) - f(x)] / h | Leibniz: dy/dx = lim (delta x->0) delta y/delta x
69
What is the alternative limit definition of the derivative at a point 'a'?
f'(a) = lim (x->a) [f(x) - f(a)] / (x - a)
70
What is the Constant Rule for differentiation?
Lagrange: (c)' = 0 | Leibniz: d/dx(c) = 0
71
What is the Power Rule for differentiation?
Lagrange: (x^n)' = nx^(n-1) | Leibniz: d/dx(x^n) = nx^(n-1)
72
What is the Sum and Difference Rule for differentiation?
Lagrange: (u ± v)' = u' ± v' | Leibniz: d/dx(u ± v) = du/dx ± dv/dx
73
What is the Product Rule for differentiation?
Lagrange: (uv)' = u'v + uv' | Leibniz: d/dx(uv) = (du/dx)v + u(dv/dx)
74
What is the Quotient Rule for differentiation?
Lagrange: (u/v)' = (u'v - uv') / v^2 | Leibniz: d/dx(u/v) = [v(du/dx) - u(dv/dx)] / v^2
75
What is the Chain Rule for composite functions?
Lagrange: [f(g(x))]' = f'(g(x)) * g'(x) | Leibniz: dy/dx = (dy/du) * (du/dx)
76
What is the derivative of sin(u) using the Chain Rule?
Lagrange: [sin(u)]' = cos(u) * u' | Leibniz: d/dx(sin u) = cos(u) * du/dx
77
What is the derivative of cos(u) using the Chain Rule?
Lagrange: [cos(u)]' = -sin(u) * u' | Leibniz: d/dx(cos u) = -sin(u) * du/dx
78
What is the derivative of tan(u) using the Chain Rule?
Lagrange: [tan(u)]' = sec^2(u) * u' | Leibniz: d/dx(tan u) = sec^2(u) * du/dx
79
What is the derivative of cot(u) using the Chain Rule?
Lagrange: [cot(u)]' = -csc^2(u) * u' | Leibniz: d/dx(cot u) = -csc^2(u) * du/dx
80
What is the derivative of sec(u) using the Chain Rule?
Lagrange: [sec(u)]' = sec(u)tan(u) * u' | Leibniz: d/dx(sec u) = sec(u)tan(u) * du/dx
81
What is the derivative of csc(u) using the Chain Rule?
Lagrange: [csc(u)]' = -csc(u)cot(u) * u' | Leibniz: d/dx(csc u) = -csc(u)cot(u) * du/dx
82
What is the derivative of e^u using the Chain Rule?
Lagrange: [e^u]' = e^u * u' | Leibniz: d/dx(e^u) = e^u * du/dx
83
What is the derivative of a^u using the Chain Rule?
Lagrange: [a^u]' = a^u * ln(a) * u' | Leibniz: d/dx(a^u) = a^u * ln(a) * du/dx
84
What is the derivative of ln(u) using the Chain Rule?
Lagrange: [ln(u)]' = (1/u) * u' | Leibniz: d/dx(ln u) = (1/u) * du/dx
85
What is the derivative of log_a(u) using the Chain Rule?
Lagrange: [loga(u)]' = [1 / (u * ln a)] * u' | Leibniz: d/dx(loga u) = [1 / (u * ln a)] * du/dx
86
What is the derivative of the absolute value |u|?
Lagrange: [|u|]' = (u / |u|) * u' | Leibniz: d/dx(|u|) = (u / |u|) * du/dx (for u != 0)
87
What is the derivative of an inverse function g(x) = f^-1(x)?
Lagrange: g'(x) = 1 / f'(g(x)) | Leibniz: dy/dx = 1 / (dx/dy)
88
What is the derivative of arcsin(u) using the Chain Rule?
Lagrange: [sin^-1(u)]' = u' / sqrt(1 - u^2) | Leibniz: d/dx(sin^-1 u) = (du/dx) / sqrt(1 - u^2)
89
What is the derivative of arccos(u) using the Chain Rule?
Lagrange: [cos^-1(u)]' = -u' / sqrt(1 - u^2) | Leibniz: d/dx(cos^-1 u) = -(du/dx) / sqrt(1 - u^2)
90
What is the derivative of arctan(u) using the Chain Rule?
Lagrange: [tan^-1(u)]' = u' / (1 + u^2) | Leibniz: d/dx(tan^-1 u) = (du/dx) / (1 + u^2)
91
What is the derivative of arccot(u) using the Chain Rule?
Lagrange: [cot^-1(u)]' = -u' / (1 + u^2) | Leibniz: d/dx(cot^-1 u) = -(du/dx) / (1 + u^2)
92
What is the derivative of arcsec(u) using the Chain Rule?
Lagrange: [sec^-1(u)]' = u' / (|u| * sqrt(u^2 - 1)) | Leibniz: d/dx(sec^-1 u) = (du/dx) / (|u| * sqrt(u^2 - 1))
93
What is the derivative of arccsc(u) using the Chain Rule?
Lagrange: [csc^-1(u)]' = -u' / (|u| * sqrt(u^2 - 1)) | Leibniz: d/dx(csc^-1 u) = -(du/dx) / (|u| * sqrt(u^2 - 1))
94
How do you find the slope dy/dx of a parametric curve?
Leibniz: dy/dx = (dy/dt) / (dx/dt)
95
How do you find the second derivative d^2y/dx^2 of a parametric curve?
Leibniz: d^2y/dx^2 = [d/dt (dy/dx)] / (dx/dt)
96
What is the formula for the slope dy/dx of a polar curve r = f(theta)?
Leibniz: dy/dx = (r'sin theta + rcos theta) / (r'cos theta - rsin theta)
97
What are the exact conditions and statement of the Extreme Value Theorem (EVT)?
CONDITIONS: f is continuous on the closed interval [a, b]. STATEMENT: f attains both an absolute maximum and an absolute minimum value on [a, b].
98
What are the exact conditions and statement of the Mean Value Theorem (MVT) for Derivatives?
CONDITIONS: f is continuous on [a, b] and differentiable on (a, b). STATEMENT: There exists a c in (a, b) such that f'(c) = (f(b)-f(a))/(b-a).
99
What are the exact conditions and statement of the Mean Value Theorem (MVT) for Integrals?
CONDITIONS: f is continuous on [a, b]. STATEMENT: There exists a c in (a, b) such that f(c) = (1/(b-a)) * Integral[a to b] f(x) dx.
100
What are the exact conditions and statement of Rolle's Theorem?
CONDITIONS: f is continuous on [a, b], differentiable on (a, b), and f(a)=f(b). STATEMENT: There exists a c in (a, b) such that f'(c) = 0.
101
Integral Property: What is the value of an integral with identical limits: integral from a to a of f(x) dx?
0
102
Integral Property: What is the result of reversing the limits of integration: integral from a to b of f(x) dx?
- integral from b to a of f(x) dx
103
Integral Property: What is the Additive Property of Integrals for integral from a to b of f(x) dx using a point c?
integral from a to c of f(x) dx + integral from c to b of f(x) dx
104
FTC Part 1 (Evaluation): State the result of integral from a to b of f'(x) dx.
f(b) - f(a)
105
FTC Part 2 (Leibniz): State the derivative of the integral: d/dx [integral from a to g(x) of f(t) dt].
f(g(x)) * g'(x)
106
FTC Part 2 (Lagrange): If F(x) = integral from a to x of f(t) dt, what is F'(x)?
f(x)
107
Basic Integral: What is the Power Rule for integration: integral of u^n du (where n != -1)?
(u^(n+1))/(n+1) + C
108
Basic Integral: What is the integral of 1/u du?
ln|u| + C
109
Basic Integral: What is the integral of e^u du?
e^u + C
110
Basic Integral: What is the integral of a^u du?
(a^u)/(ln a) + C
111
Trig Integral: What is the integral of sin(u) du?
-cos(u) + C
112
Trig Integral: What is the integral of cos(u) du?
sin(u) + C
113
Trig Integral: What is the integral of sec^2(u) du?
tan(u) + C
114
Trig Integral: What is the integral of csc^2(u) du?
-cot(u) + C
115
Trig Integral: What is the integral of sec(u)tan(u) du?
sec(u) + C
116
Trig Integral: What is the integral of csc(u)cot(u) du?
-csc(u) + C
117
Trig Integral: What is the integral of tan(u) du?
-ln|cos u| + C (or ln|sec u| + C)
118
Trig Integral: What is the integral of cot(u) du?
ln|sin u| + C
119
Inverse Trig Integral: What is the integral of du / sqrt(a^2 - u^2)?
arcsin(u/a) + C
120
Inverse Trig Integral: What is the integral of du / (a^2 + u^2)?
(1/a) * arctan(u/a) + C
121
Inverse Trig Integral: What is the integral of du / (u * sqrt(u^2 - a^2))?
(1/a) * arcsec(|u|/a) + C
122
Integration Technique: What is the formula for Integration by Parts: integral of u dv?
uv - integral of v du
123
Integration Technique: What does the acronym LIATE stand for when choosing 'u' for Integration by Parts?
Logarithmic, Inverse Trig, Algebraic, Trig, Exponential
124
Integration Application: What is the formula for the Average Value of a function f(x) on the interval [a, b]?
(1 / (b - a)) * integral from a to b of f(x) dx
125
What is the relationship between Velocity v(t) and Position s(t)?
v(t) = s'(t) (The first derivative of position)
126
What is the relationship between Acceleration a(t) and Velocity v(t)?
a(t) = v'(t) = s''(t) (The derivative of velocity or second derivative of position)
127
What is the formula for Speed?
Speed = |v(t)| (The absolute value of velocity)
128
What is the formula for Displacement from time t1 to t2?
Displacement = integral from t1 to t2 of v(t) dt
129
What is the formula for Total Distance Traveled from time t1 to t2?
Total Distance = integral from t1 to t2 of |v(t)| dt
130
What is the formula for Area between curves with respect to x?
Area = integral from a to b of [Top(x) - Bottom(x)] dx
131
What is the formula for Area between curves with respect to y?
Area = integral from c to d of [Right(y) - Left(y)] dy
132
What is the formula for Volume using the Disk Method?
V = pi * integral from a to b of [R(x)]^2 dx
133
What is the formula for Volume using the Washer Method?
V = pi * integral from a to b of ([R(x)]^2 - [r(x)]^2) dx
134
What is the general formula for Volume by Cross Sections?
V = integral from a to b of A(x) dx
135
What is the Area A(x) for a Square cross section?
A(x) = [side(x)]^2
136
What is the Area A(x) for a Semicircle cross section?
A(x) = (pi / 8) * [diameter(x)]^2
137
What is the Area A(x) for an Equilateral Triangle cross section?
A(x) = (sqrt(3) / 4) * [side(x)]^2
138
What is the formula for Arc Length (Cartesian/Function form)?
L = integral from a to b of sqrt(1 + [f'(x)]^2) dx
139
What is the formula for Arc Length (Parametric form)?
L = integral from t1 to t2 of sqrt([x'(t)]^2 + [y'(t)]^2) dt
140
What is the formula for Arc Length (Polar form)?
L = integral from alpha to beta of sqrt(r^2 + [dr/dtheta]^2) dtheta
141
What is the formula for Area in Polar Coordinates?
A = (1/2) * integral from alpha to beta of [r(theta)]^2 dtheta
142
How do you determine if a particle is speeding up?
Velocity v(t) and Acceleration a(t) must have the SAME sign (both + or both -)
143
How do you determine if a particle is slowing down?
Velocity v(t) and Acceleration a(t) must have OPPOSITE signs
144
What is the definition of a Differential Equation (DE)?
An equation that involves an unknown function and one or more of its derivatives.
145
What is a 'General Solution' to a differential equation?
A solution that includes an arbitrary constant (C) representing a family of curves.
146
What is a 'Particular Solution' to a differential equation?
A specific solution where the constant (C) is determined using an initial condition (x0, y0).
147
What is the first step in the 'Separation of Variables' method for dy/dx = f(x)g(y)?
Rewrite the equation so all y-terms are on one side and all x-terms are on the other: (1/g(y)) dy = f(x) dx.
148
What is a Slope Field?
A graphical representation of the slopes (dy/dx) of a differential equation at various points (x, y).
149
What does a horizontal segment in a slope field indicate?
It indicates that the derivative dy/dx is equal to zero at that point.
150
What is the iterative formula for Euler's Method to find the next x-value (x_new)?
x_new = x_old + delta x
151
What is the iterative formula for Euler's Method to find the next y-value (y_new)?
y_new = y_old + (dy/dx)|(x_old, y_old) * delta x
152
What is the differential equation for Exponential Growth/Decay?
dy/dt = ky
153
What is the general solution to the exponential growth/decay equation dy/dt = ky?
y = Ce^(kt)
154
What is the Logistic Growth differential equation (Standard AP Form)?
dP/dt = kP(1 - P/M) where M is the carrying capacity.
155
What is the Logistic Growth differential equation (Alternative Form)?
dP/dt = kP(M - P) where M is the carrying capacity.
156
What is the general solution to the Logistic Growth equation dP/dt = kP(1 - P/M)?
P(t) = M / (1 + Ae^(-kt))
157
In a Logistic Growth model at what population value (P) is the growth rate at its maximum?
P = M/2 (Half of the carrying capacity).
158
In a Logistic Growth model what is the limit of P(t) as t approaches infinity?
M (The carrying capacity).
159
What is the second derivative (d^2y/dx^2) of a differential equation used for?
To determine the concavity of the solution curve at a specific point.
160
How do you verify if a given function is a solution to a differential equation?
Substitute the function and its derivatives into the differential equation and check if the equation holds true.
161
What is the general form of a Geometric Series?
Form: sum from n=0 to infinity of (a * r^n)
162
When does a Geometric Series converge?
Converges if |r| < 1.
163
What is the sum formula for a convergent Geometric Series?
S = a / (1 - r) where 'a' is the first term.
164
What is the Nth Term Test for Divergence?
If lim n->infinity of (a_n) is NOT equal to 0, then the series diverges.
165
What are the 3 conditions required to use the Integral Test?
The function f(x) must be continuous, positive, and decreasing for x >= 1.
166
What is the result of the Integral Test?
The integral from 1 to infinity of f(x) dx converges if and only if the series sum(a_n) converges.
167
When does a P-Series (sum of 1/n^p) converge?
Converges if p > 1 (Diverges if p <= 1).
168
What is the Direct Comparison Test?
Given 0 < an < bn: If the 'big' series (bn) converges, then (an) converges. If the 'small' series (an) diverges, then (bn) diverges.
169
What is the Limit Comparison Test?
If lim n->infinity of (an / bn) = L (where L is finite and positive), then both series either both converge or both diverge.
170
What are the 2 conditions for the Alternating Series Test (AST)?
1. lim n->infinity of bn = 0 AND 2. b(n+1) <= b_n (terms are decreasing).
171
What is the Ratio Test formula and its conditions?
lim n->infinity of |a(n+1) / an| = L. Converges if L < 1; Diverges if L > 1; Fails if L = 1.
172
What is the Root Test formula and its conditions?
lim n->infinity of nth-root(|a_n|) = L. Converges if L < 1; Diverges if L > 1.
173
Define Absolute Convergence.
A series sum(an) converges absolutely if the series of absolute values sum(|an|) converges.
174
Define Conditional Convergence.
A series sum(an) converges conditionally if sum(an) converges but sum(|a_n|) diverges.
175
What is the formula for a Taylor Series centered at x = c?
f(x) = sum from n=0 to infinity of [ f^(n)(c) / n! * (x - c)^n ]
176
What is the formula for a Maclaurin Series?
f(x) = sum from n=0 to infinity of [ f^(n)(0) / n! * x^n ] (This is a Taylor series centered at x = 0).
177
What is the Maclaurin series expansion for e^x?
1 + x + (x^2 / 2!) + (x^3 / 3!) + ... (Interval: -infinity < x < infinity)
178
What is the Maclaurin series expansion for sin(x)?
x - (x^3 / 3!) + (x^5 / 5!) - ... (Interval: -infinity < x < infinity)
179
What is the Maclaurin series expansion for cos(x)?
1 - (x^2 / 2!) + (x^4 / 4!) - ... (Interval: -infinity < x < infinity)
180
What is the Maclaurin series expansion for 1 / (1 - x)?
1 + x + x^2 + x^3 + ... (Interval: -1 < x < 1)
181
What is the Alternating Series Error Bound?
|S - Sn| <= |a(n+1)| (The error is less than or equal to the absolute value of the first neglected term).
182
What is the Lagrange Error Bound formula?
|R_n(x)| <= [ M / (n + 1)! ] * |x - c|^(n+1)
183
In the Lagrange Error Bound, what does 'M' represent?
M is the maximum value of the (n+1)-th derivative of f on the interval between the center c and the point x.
184
Define Radius of Convergence (R).
The distance from the center 'c' to the boundary of the interval where the series converges.
185
Define Interval of Convergence.
The set of all real numbers x for which the power series converges (found using Ratio Test + checking endpoints).
186
What is a Power Series?
A series of the form sum(cn * (x - c)^n) where cn are coefficients and c is the center.
AP Calculus BC
flashcards
Decks in class (11)
# Cards
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Unit 0: Review12
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Unit 01: Limits & Continuity16
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Unit 02: Differentiation - Definition and Fundamental Properties14
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Unit 03: Differentiation - Composite, Implicit, and Inverse Functions10
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Unit 04: Contextual Applications of Differentiation14
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Unit 05: Analytical Applications of Differentiation14
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Unit 06 Part 1: Integration and Accumulation of Change84
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Unit 06 Part 2: Integration Rules75
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Unit 07: Differential Equations33
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Unit 08: Applications of Integration56
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Formula List186
