| 9742879873 | Double Angle Formula for cos²(θ) | |  | 0 |
| 9742879874 | Double Angle Formula for sin²(θ) | |  | 1 |
| 9742879875 | sin(0)= | |  | 2 |
| 9742879876 | sin(π/4) | |  | 3 |
| 9742879877 | sin⁻¹(-1) | |  | 4 |
| 9742879878 | tan⁻¹(-1) | |  | 5 |
| 9742879879 | 1+cot²(θ) | |  | 6 |
| 9742879880 | 1+tan²(θ) | |  | 7 |
| 9742879881 | sin(2θ) | |  | 8 |
| 9742879882 | cos(2θ) | |  | 9 |
| 9742879883 | log(AB) | |  | 10 |
| 9742879884 | log(A / B) | |  | 11 |
| 9742879885 | log(A) ^ x | |  | 12 |
| 9742879886 | e^(ln(x)) | |  | 13 |
| 9742879887 | ln(x) / ln(a) | |  | 14 |
| 9742879888 | Simplify the expression into one log:
2 ln(x) + ln(x+1) - ln(x-1) | |  | 15 |
| 9742879889 | For what value of x is there a
hole, and for what value of x
is there a vertical asymptote?
f(x) = ((x - a)(x - b))/ ((x - a)(x - c)) | |  | 16 |
| 9742879890 | Definition of the Derivative
(Using the limit as h→0) | |  | 17 |
| 9742879891 | lim x→₀ sin(x)/x | |  | 18 |
| 9742879892 | lim x→∞ tan⁻¹(x) | |  | 19 |
| 9742879893 | First derivative test for a local max of f at x = a | |  | 20 |
| 9742879894 | First derivative test for a local min of f at x = a | |  | 21 |
| 9742879895 | Second derivative test for a local max of f at x = a | |  | 22 |
| 9742879896 | Second derivative test for a local min of f at x = a | |  | 23 |
| 9742879897 | Test for max and mins of f on [a, b] | |  | 24 |
| 9742879898 | Inflection Points | |  | 25 |
| 9742879899 | ƒ'(x) < 0 | |  | 26 |
| 9742879900 | ƒ''(x) < 0 or ƒ'(x) is decreasing | |  | 27 |
| 9742879901 | ƒ'(x) > 0 | |  | 28 |
| 9742879902 | ƒ''(x) > 0 or ƒ'(x) is increasing | |  | 29 |
| 9742879903 | Intermediate Value Theorem (IVT) | |  | 30 |
| 9742879904 | Mean Value Theorem (MVT) | |  | 31 |
| 9742879905 | Rolle's Theorem | |  | 32 |
| 9742879906 | Squeeze Theorem | |  | 33 |
| 9742879907 | ƒ(x) is continuous at x = a if... | |  | 34 |
| 9742879908 | Extreme Value Theorem | |  | 35 |
| 9742879909 | Critical Points | |  | 36 |
| 9742879910 | Three types of discontinuities. | |  | 37 |
| 9742879911 | ƒ(x) is differentiable at x = a if... | |  | 38 |
| 9742879912 | Three conditions where ƒ(x) is not differentiable | |  | 39 |
| 9742879913 | Average rate of change of ƒ(x) over [a, b] | |  | 40 |
| 9742879914 | Instantaneous rate of change of ƒ(a) | |  | 41 |
| 9742879915 | d/dx ( tan⁻¹ ( x ) ) | |  | 42 |
| 9742879916 | d/dx ( sin⁻¹ ( x ) ) | |  | 43 |
| 9742879917 | d/dx ( e ^ x ) | |  | 44 |
| 9742879918 | d/dx ( ln x ) | |  | 45 |
| 9742879919 | d/dx ( a ^ x ) | |  | 46 |
| 9742879920 | d/dx ( sin x ) | |  | 47 |
| 9742879921 | d/dx ( cos x ) | |  | 48 |
| 9742879922 | d/dx ( tan x ) | |  | 49 |
| 9742879923 | d/dx ( sec x ) | |  | 50 |
| 9742879924 | d/dx ( csc x ) | |  | 51 |
| 9742879925 | d/dx ( cot x ) | |  | 52 |
| 9742879926 | Product Rule | |  | 53 |
| 9742879927 | Quotient Rule | |  | 54 |
| 9742879928 | Chain Rule | |  | 55 |
| 9742879929 | d/dx (ƒ(x)³) | |  | 56 |
| 9742879930 | d/dx ( ln ƒ(x) ) | |  | 57 |
| 9742879931 | d/dx (e ^ ƒ(x) ) | |  | 58 |
| 9742879932 | Derivative of the Inverse of ƒ(x) | |  | 59 |
| 9742879933 | Implicit Differentiation
Find dy/dx:
x²/9+y²/4=1 | |  | 60 |
| 9742879934 | Equation of a line in point-slope form | |  | 61 |
| 9742879935 | Equation of the tangent line
to y = ƒ(x)
at x = a | |  | 62 |
| 9742879936 | A normal line to a curve is... | |  | 63 |
| 9742879937 | Velocity of a point moving along a line with position at time t given by d(t) | |  | 64 |
| 9742879938 | Speed of a point moving along a line | |  | 65 |
| 9742879939 | Average velocity
of s over [a, b] | |  | 66 |
| 9742879940 | Average speed
of s over [a, b] | |  | 67 |
| 9742879941 | Average acceleration
given v over [a, b] | |  | 68 |
| 9742879942 | An object in motion is at rest when... | |  | 69 |
| 9742879943 | An object in motion reverses direction when... | |  | 70 |
| 9742879944 | Acceleration of a point moving along a line with position at time t given by d(t) | |  | 71 |
| 9742879945 | How to tell if a point moving along the x-axis with velocity v(t) is speeding up or slowing down at some time t? | |  | 72 |
| 9742879946 | Position at time t = b of a particle moving along a line given velocity v(t) and position s(t) at time t = a | |  | 73 |
| 9742879947 | Displacement of a particle moving along a line with velocity v(t) for a ≤ t ≤ b. | |  | 74 |
| 9742880076 | Total distance traveled by a particle moving along a line with velocity v(t) for a ≤ t ≤ b | ... |  | 75 |
| 9742879948 | The total change in ƒ(x) over [a, b] in terms of the rate of change, ƒ'(x) | |  | 76 |
| 9742879949 | Graph of y = 1/x | |  | 77 |
| 9742879950 | Graph of y = e ^ (kx) | |  | 78 |
| 9742879951 | Graph of y = ln x | |  | 79 |
| 9742879952 | Graph of y = sin x | |  | 80 |
| 9742879953 | Graph of y = cos x | |  | 81 |
| 9742879954 | Graph of y = tan x | |  | 82 |
| 9742879955 | Graph of y = tan⁻¹ x | |  | 83 |
| 9742879956 | Graph of y = √(1 - x²) | |  | 84 |
| 9742879957 | Graph of x²/a² + y²/b² = 1 | |  | 85 |
| 9742879958 | L'Hopital's Rule | |  | 86 |
| 9742879959 | To find the limits of
indeterminate forms:
∞ × 0 | |  | 87 |
| 9742879960 | To find the limits of
indeterminate forms:
0 ^ 0, 1 ^ ∞, ∞ ^ 0 | |  | 88 |
| 9742879961 | If ƒ(x) is increasing, then a left Riemann sum ... | |  | 89 |
| 9742879962 | If ƒ(x) is decreasing, then a left Riemann sum ... | |  | 90 |
| 9742879963 | If ƒ(x) is increasing, then a right Riemann sum ... | |  | 91 |
| 9742879964 | If ƒ(x) is decreasing, then a right Riemann sum ... | |  | 92 |
| 9742879965 | If ƒ(x) is concave up, then the trapezoidal approximation of the integral... | |  | 93 |
| 9742879966 | If ƒ(x) is concave down, then the trapezoidal approximation of the integral... | |  | 94 |
| 9742879967 | If ƒ(x) is concave up, then a midpoint Riemann sum... | |  | 95 |
| 9742879968 | If ƒ(x) is concave down, then a midpoint Riemann sum... | |  | 96 |
| 9742879969 | Area of a trapezoid | |  | 97 |
| 9742879970 | If ƒ(x) is concave down then the linear approximation... | |  | 98 |
| 9742879971 | If ƒ(x) is concave up then the linear approximation... | |  | 99 |
| 9742879972 | The Fundamental Theorem of Calculus (Part I) | |  | 100 |
| 9742879973 | The Fundamental Theorem of Calculus (Part II) | |  | 101 |
| 9742879974 | ∫ x ^ n dx = | |  | 102 |
| 9742879975 | ∫ e ^ x dx = | |  | 103 |
| 9742879976 | ∫ 1/x dx = | |  | 104 |
| 9742879977 | ∫ sin x dx = | |  | 105 |
| 9742879978 | ∫ cos x dx = | |  | 106 |
| 9742879979 | ∫ sec² x dx = | |  | 107 |
| 9742879980 | ∫ a ^ x dx = | |  | 108 |
| 9742879981 | ∫ tan x dx = | |  | 109 |
| 9742879982 | ∫ 1 / (x² + 1) dx = | |  | 110 |
| 9742879983 | ∫ 1 / √(1 - x² ) dx = | |  | 111 |
| 9742879984 | The average value of f from x = a to x = b
(Mean Value Theorem for Integrals) | |  | 112 |
| 9742879985 | Integral equation for a horizontal shift of 1 unit to the right. | |  | 113 |
| 9742879986 | Adding adjacent integrals | |  | 114 |
| 9742879987 | Swapping the bounds of an integral | |  | 115 |
| 9742879988 | Exponential Growth
Solution of
dy/dt = kP
P(0) = P₀ | |  | 116 |
| 9742879989 | lim n→∞ (1 + 1/n) ^ n | |  | 117 |
| 9742879990 | Steps to solve a differential equation | |  | 118 |
| 9742879991 | To find the area between 2 curves using vertical rectangles (dx) | |  | 119 |
| 9742879992 | To find the area between 2 curves using horizontal rectangles (dy) | |  | 120 |
| 9742879993 | Volume of a disc; rotated about a horizontal line | |  | 121 |
| 9742879994 | Volume of a washer; rotated about a horizontal line | |  | 122 |
| 9742879995 | Volume of a disc; rotated about a vertical line | |  | 123 |
| 9742879996 | Volume of a washer; rotated about a vertical line | |  | 124 |
| 9742879997 | Volume of solid if cross sections perpendicular to the
x-axis are squares | |  | 125 |
| 9742879998 | Volume of solid if cross sections perpendicular to the
x-axis are isosceles right triangles | |  | 126 |
| 9742879999 | Volume of solid if cross sections perpendicular to the
x-axis are equilateral triangles | |  | 127 |
| 9742880000 | Volume of solid if cross sections perpendicular to the
x-axis are semicircles | |  | 128 |
| 9742880001 | Volume of a prism | |  | 129 |
| 9742880002 | Volume of a cylinder | |  | 130 |
| 9742880003 | Volume of a pyramid | |  | 131 |
| 9742880004 | Volume of a cone | |  | 132 |
| 9742880005 | Volume of a sphere | |  | 133 |
| 9742880006 | Surface Area of a cylinder | |  | 134 |
| 9742880007 | Surface Area of a sphere | |  | 135 |
| 9742880008 | Area of a Sector
(in radians) | |  | 136 |
| 9742880009 | Slope of a parametric curve
x = x(t) and y = y(t) | |  | 137 |
| 9742880010 | Horizontal Tangent
of a parametric curve | |  | 138 |
| 9742880011 | Vertical Tangent
of a parametric curve | |  | 139 |
| 9742880012 | Second Derivative
of a parametric curve | |  | 140 |
| 9742880013 | Velocity vector of a particle moving in the plane x = x(t) and y = y(t) | |  | 141 |
| 9742880014 | Acceleration vector of a particle moving in the plane
x = x(t) and y = y(t) | |  | 142 |
| 9742880015 | Speed of a particle moving in the plane
x = x(t) and y = y(t) | |  | 143 |
| 9742880016 | Distance traveled (Arc Length) by a particle moving in the plane with a ≤ t ≤ b x = x(t) and y = y(t) | |  | 144 |
| 9742880017 | Position at time t = b of a particle moving in the plane given x(a), y(a), x′(t), and y′(t). | |  | 145 |
| 9742880018 | Magnitude of a vector in terms of the x and y components | |  | 146 |
| 9742880019 | Graph of
θ = c
(c is a constant) | |  | 147 |
| 9742880020 | Graph of
r = θ | |  | 148 |
| 9742880021 | Graphs of:
r = c
r = c sin(θ)
r = c cos(θ)
(c is a constant) | |  | 149 |
| 9742880022 | Graphs of:
r = sin(k θ)
r = cos(k θ)
(k is a constant) | |  | 150 |
| 9742880023 | Graph of:
r = 1 + cos(θ) | |  | 151 |
| 9742880024 | Graph of:
r = 1 + 2 cos(θ) | |  | 152 |
| 9742880025 | Slope of polar graph r (θ) | |  | 153 |
| 9742880026 | Area enclosed by r = f(θ),
α ≤ θ ≤ β | |  | 154 |
| 9742880027 | Double Angle Formula for cos²θ | |  | 155 |
| 9742880028 | Double Angle Formula for sin²θ | |  | 156 |
| 9742880029 | dx/dθ < 0 | |  | 157 |
| 9742880030 | dx/dθ > 0 | |  | 158 |
| 9742880031 | dy/dθ < 0 | |  | 159 |
| 9742880032 | dy/dθ > 0 | |  | 160 |
| 9742880033 | Convert from polar (r,θ) to rectangular (x,y) | |  | 161 |
| 9742880034 | Convert from rectangular (x,y) to polar (r,θ) | |  | 162 |
| 9742880035 | Horizontal Tangent of a Polar Graph | |  | 163 |
| 9742880036 | Vertical Tangent of a Polar Graph | |  | 164 |
| 9742880037 | Integration by Parts Formula | |  | 165 |
| 9742880038 | ∫ lnx dx = ? | |  | 166 |
| 9742880039 | Improper Integral:
∫ 1/x² dx
bounds: [0,1] | |  | 167 |
| 9742880040 | Improper Integral:
∫ f(x) dx
bounds: [0,∞] | |  | 168 |
| 9742880041 | Arc length
of a function f(x) from
x = a to x = b | |  | 169 |
| 9742880042 | Arc length
of a polar graph r
0 ≤ θ ≤ π | |  | 170 |
| 9742880043 | Arc Length
of a graph defined parametrically with
a ≤ t ≤ b
x = x(t) and y = y(t) | |  | 171 |
| 9742880044 | Differential equation for exponential growth
dP/dt = ? | |  | 172 |
| 9742880045 | Solution of a differential equation for exponential growth | |  | 173 |
| 9742880046 | Differential equation for decay
dP/dt = ? | |  | 174 |
| 9742880047 | Solution of a differential equation for decay | |  | 175 |
| 9742880048 | Logistic differential equation
dP/dt = ? | |  | 176 |
| 9742880049 | Solution of a logistic differential equation | |  | 177 |
| 9742880050 | Graph of a Logistic Function
(include inflection pt.) | |  | 178 |
| 9742880051 | Euler's Method for solving
y' = F (x,y)
with initial point (x₀ , y₀) | |  | 179 |
| 9742880052 | Power Series for
f(x) = 1 / (1 - x)
(include IOC) | |  | 180 |
| 9742880053 | Power Series for
f(x) = tan⁻¹ x
(include IOC) | |  | 181 |
| 9742880054 | Power Series for
f(x) = ln (1 + x)
(include IOC) | |  | 182 |
| 9742880055 | Taylor Series for f(x) about x = 0
(Maclaurin Series) | |  | 183 |
| 9742880056 | Taylor Series for f(x) about x = c | |  | 184 |
| 9742880057 | Maclaurin Series for
f (x) = e∧x
(include IOC) | |  | 185 |
| 9742880058 | Maclaurin Series for
f (x) = sin x
(include IOC) | |  | 186 |
| 9742880059 | Maclaurin Series for
f (x) = cos x
(include IOC) | |  | 187 |
| 9742880060 | Error for the partial sum, Sn, of an infinite series S | |  | 188 |
| 9742880061 | Error bound of an alternating series | |  | 189 |
| 9742880062 | Lagrange error bound | |  | 190 |
| 9742880063 | Geometric sequence
(def. and conv. property) | |  | 191 |
| 9742880064 | Harmonic Series
(def. and conv. property) | |  | 192 |
| 9742880065 | p-series
(def. and conv. property) | |  | 193 |
| 9742880066 | Divergence Test | |  | 194 |
| 9742880067 | If lim n→∞ a(sub n) = 0,
then ∑ a(sub n) for n from 1 to ∞ ... | |  | 195 |
| 9742880068 | Integral Test | |  | 196 |
| 9742880069 | Alternating Series Test | |  | 197 |
| 9742880070 | Direct Comparison Test | |  | 198 |
| 9742880071 | Limit Comparison Test | |  | 199 |
| 9742880072 | Ratio Test | |  | 200 |
| 9742880073 | n-th Root Test | |  | 201 |
| 9742880074 | Interval of Convergence (IOC) | |  | 202 |
| 9742880075 | Radius of Convergence | |  | 203 |