Statesville Christian School AP Calculus Class
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| 8574689923 | Intermediate Value Theorem | If f(1)=-4 and f(6)=9, then there must be a x-value between 1 and 6 where f crosses the x-axis. | 0 | |
| 8574689924 | Average Rate of Change | Slope of secant line between two points, use to estimate instantanous rate of change at a point. | 1 | |
| 8574689925 | Instantenous Rate of Change | Slope of tangent line at a point, value of derivative at a point | 2 | |
| 8574689926 | Formal definition of derivative |  | 3 | |
| 8574689927 | Alternate definition of derivative | limit as x approaches a of [f(x)-f(a)]/(x-a) | 4 | |
| 8574689928 | When f '(x) is positive, f(x) is | increasing | 5 | |
| 8574689929 | When f '(x) is negative, f(x) is | decreasing | 6 | |
| 8574689930 | When f '(x) changes from negative to positive, f(x) has a | relative minimum | 7 | |
| 8574689931 | When f '(x) changes from positive to negative, f(x) has a | relative maximum | 8 | |
| 8574689932 | When f '(x) is increasing, f(x) is | concave up | 9 | |
| 8574689933 | When f '(x) is decreasing, f(x) is | concave down | 10 | |
| 8574689934 | When f '(x) changes from increasing to decreasing or decreasing to increasing, f(x) has a | point of inflection | 11 | |
| 8574689935 | When is a function not differentiable | corner, cusp, vertical tangent, discontinuity | 12 | |
| 8574689936 | Product Rule | uv' + vu' | 13 | |
| 8574689937 | Quotient Rule | (uv'-vu')/v² | 14 | |
| 8574689938 | Chain Rule | f '(g(x)) g'(x) | 15 | |
| 8574689939 | y = x cos(x), state rule used to find derivative | product rule | 16 | |
| 8574689940 | y = ln(x)/x², state rule used to find derivative | quotient rule | 17 | |
| 8574689941 | y = cos²(3x) | chain rule | 18 | |
| 8574689942 | Particle is moving to the right/up | velocity is positive | 19 | |
| 8574689943 | Particle is moving to the left/down | velocity is negative | 20 | |
| 8574689944 | absolute value of velocity | speed | 21 | |
| 8574689945 | y = sin(x), y' = | y' = cos(x) | 22 | |
| 8574689946 | y = cos(x), y' = | y' = -sin(x) | 23 | |
| 8574689947 | y = tan(x), y' = | y' = sec²(x) | 24 | |
| 8574689948 | y = csc(x), y' = | y' = -csc(x)cot(x) | 25 | |
| 8574689949 | y = sec(x), y' = | y' = sec(x)tan(x) | 26 | |
| 8574689950 | y = cot(x), y' = | y' = -csc²(x) | 27 | |
| 8574689951 | y = sin⁻¹(x), y' = | y' = 1/√(1 - x²) | 28 | |
| 8574689952 | y = cos⁻¹(x), y' = | y' = -1/√(1 - x²) | 29 | |
| 8574689953 | y = tan⁻¹(x), y' = | y' = 1/(1 + x²) | 30 | |
| 8574689954 | y = cot⁻¹(x), y' = | y' = -1/(1 + x²) | 31 | |
| 8574689955 | y = e^x, y' = | y' = e^x | 32 | |
| 8574689956 | y = a^x, y' = | y' = a^x ln(a) | 33 | |
| 8574689957 | y = ln(x), y' = | y' = 1/x | 34 | |
| 8574689958 | y = log (base a) x, y' = | y' = 1/(x lna) | 35 | |
| 8574689959 | To find absolute maximum on closed interval [a, b], you must consider... | critical points and endpoints | 36 | |
| 8574689960 | mean value theorem | if f(x) is continuous and differentiable, slope of tangent line equals slope of secant line at least once in the interval (a, b) f '(c) = [f(b) - f(a)]/(b - a) | 37 | |
| 8574689961 | If f '(x) = 0 and f"(x) > 0, | f(x) has a relative minimum | 38 | |
| 8574689962 | If f '(x) = 0 and f"(x) < 0, | f(x) has a relative maximum | 39 | |
| 8574689963 | Linearization | use tangent line to approximate values of the function | 40 | |
| 8574689964 | rate | derivative | 41 | |
| 8574689965 | left riemann sum | use rectangles with left-endpoints to evaluate integral (estimate area) | 42 | |
| 8574689966 | right riemann sum | use rectangles with right-endpoints to evaluate integrals (estimate area) | 43 | |
| 8574689967 | trapezoidal rule | use trapezoids to evaluate integrals (estimate area) | 44 | |
| 8574689968 | [(h1 - h2)/2]*base | area of trapezoid | 45 | |
| 8574689969 | definite integral | has limits a & b, find antiderivative, F(b) - F(a) | 46 | |
| 8574689970 | indefinite integral | no limits, find antiderivative + C, use inital value to find C | 47 | |
| 8574689971 | area under a curve | ∫ f(x) dx integrate over interval a to b | 48 | |
| 8574689972 | area above x-axis is | positive | 49 | |
| 8574689973 | area below x-axis is | negative | 50 | |
| 8574689974 | average value of f(x) | = 1/(b-a) ∫ f(x) dx on interval a to b | 51 | |
| 8574689975 | If g(x) = ∫ f(t) dt on interval 2 to x, then g'(x) = | g'(x) = f(x) | 52 | |
| 8574689976 | Fundamental Theorem of Calculus | ∫ f(x) dx on interval a to b = F(b) - F(a) | 53 | |
| 8574689977 | To find particular solution to differential equation, dy/dx = x/y | separate variables, integrate + C, use initial condition to find C, solve for y | 54 | |
| 8574689978 | To draw a slope field, | plug (x,y) coordinates into differential equation, draw short segments representing slope at each point | 55 | |
| 8574689979 | slope of horizontal line | zero | 56 | |
| 8574689980 | slope of vertical line | undefined | 57 | |
| 8574689981 | methods of integration | substitution, parts, partial fractions | 58 | |
| 8574689982 | use substitution to integrate when | a function and it's derivative are in the integrand | 59 | |
| 8574689983 | use integration by parts when | two different types of functions are multiplied | 60 | |
| 8574689984 | ∫ u dv = | uv - ∫ v du | 61 | |
| 8574689985 | use partial fractions to integrate when | integrand is a rational function with a factorable denominator | 62 | |
| 8574689986 | dP/dt = kP(M - P) | logistic differential equation, M = carrying capacity | 63 | |
| 8574689987 | P = M / (1 + Ae^(-Mkt)) | logistic growth equation | 64 | |
| 8574689988 | given rate equation, R(t) and inital condition when t = a, R(t) = y₁ find final value when t = b | y₁ + Δy = y Δy = ∫ R(t) over interval a to b | 65 | |
| 8574689989 | given v(t) and initial position t = a, find final position when t = b | s₁+ Δs = s Δs = ∫ v(t) over interval a to b | 66 | |
| 8574689990 | given v(t) find displacement | ∫ v(t) over interval a to b | 67 | |
| 8574689991 | given v(t) find total distance travelled | ∫ abs[v(t)] over interval a to b | 68 | |
| 8574689992 | area between two curves | ∫ f(x) - g(x) over interval a to b, where f(x) is top function and g(x) is bottom function | 69 | |
| 8574689993 | volume of solid with base in the plane and given cross-section | ∫ A(x) dx over interval a to b, where A(x) is the area of the given cross-section in terms of x | 70 | |
| 8574689994 | volume of solid of revolution - no washer | π ∫ r² dx over interval a to b, where r = distance from curve to axis of revolution | 71 | |
| 8574689995 | volume of solid of revolution - washer | π ∫ R² - r² dx over interval a to b, where R = distance from outside curve to axis of revolution, r = distance from inside curve to axis of revolution | 72 | |
| 8574689996 | length of curve | ∫ √(1 + (dy/dx)²) dx over interval a to b | 73 | |
| 8574689997 | L'Hopitals rule | use to find indeterminate limits, find derivative of numerator and denominator separately then evaluate limit | 74 | |
| 8574689998 | indeterminate forms | 0/0, ∞/∞, ∞*0, ∞ - ∞, 1^∞, 0⁰, ∞⁰ | 75 | |
| 8574689999 | 6th degree Taylor Polynomial | polynomial with finite number of terms, largest exponent is 6, find all derivatives up to the 6th derivative | 76 | |
| 8574690000 | Taylor series | polynomial with infinite number of terms, includes general term | 77 | |
| 8574690001 | nth term test | if terms grow without bound, series diverges | 78 | |
| 8574690002 | alternating series test | lim as n approaches zero of general term = 0 and terms decrease, series converges | 79 | |
| 8574690003 | converges absolutely | alternating series converges and general term converges with another test | 80 | |
| 8574690004 | converges conditionally | alternating series converges and general term diverges with another test | 81 | |
| 8574690005 | ratio test | lim as n approaches ∞ of ratio of (n+1) term/nth term > 1, series converges | 82 | |
| 8574690006 | find interval of convergence | use ratio test, set > 1 and solve absolute value equations, check endpoints | 83 | |
| 8574690007 | find radius of convergence | use ratio test, set > 1 and solve absolute value equations, radius = center - endpoint | 84 | |
| 8574690008 | integral test | if integral converges, series converges | 85 | |
| 8574690009 | limit comparison test | if lim as n approaches ∞ of ratio of comparison series/general term is positive and finite, then series behaves like comparison series | 86 | |
| 8574690010 | geometric series test | general term = a₁r^n, converges if -1 < r < 1 | 87 | |
| 8574690011 | p-series test | general term = 1/n^p, converges if p > 1 | 88 | |
| 8574690012 | derivative of parametrically defined curve x(t) and y(t) | dy/dx = dy/dt / dx/dt | 89 | |
| 8574690013 | second derivative of parametrically defined curve | find first derivative, dy/dx = dy/dt / dx/dt, then find derivative of first derivative, then divide by dx/dt | 90 | |
| 8574690014 | length of parametric curve | ∫ √ (dx/dt)² + (dy/dt)² over interval from a to b | 91 | |
| 8574690015 | given velocity vectors dx/dt and dy/dt, find speed | √(dx/dt)² + (dy/dt)² not an integral! | 92 | |
| 8574690016 | given velocity vectors dx/dt and dy/dt, find total distance travelled | ∫ √ (dx/dt)² + (dy/dt)² over interval from a to b | 93 | |
| 8574690017 | area inside polar curve | 1/2 ∫ r² over interval from a to b, find a & b by setting r = 0, solve for theta | 94 | |
| 8574690018 | area inside one polar curve and outside another polar curve | 1/2 ∫ R² - r² over interval from a to b, find a & b by setting equations equal, solve for theta. | 95 | |
| 8574690019 | Product rule Derivatives |  | 96 | |
| 8574690020 | Volume of Disc |  | 97 | |
| 8574690021 | Volume of Washer |  | 98 | |
| 8574690022 | Volume of Shell |  | 99 | |
| 8574690023 | Volume of Cross Section |  | 100 | |
| 8574690024 | Second Fundamental Theorem |  | 101 | |
| 8574690025 | Area of Trapezoid |  | 102 | |
| 8574690026 | Trapezoidal Rule |  | 103 | |
| 8574690027 | Alt. Series Error: |  | 104 | |
| 8574690028 | Lagrange Error |  | 105 | |
| 8574690029 | Integral of u'/u |  | 106 | |
| 8574690030 | Integral of a^x |  | 107 | |
| 8574690031 | Integral of sin x |  | 108 | |
| 8574690032 | Integral of cos x |  | 109 | |
| 8574690033 | Integral of sec^2 x |  | 110 | |
| 8574690034 | Integral of tan x |  | 111 | |
| 8574690035 | Integral of cot x |  | 112 | |
| 8574690036 | Integral of sec x tan x |  | 113 | |
| 8574690037 | Integral of csc^2 x |  | 114 | |
| 8574690038 | Integral of csc x cot x |  | 115 | |
| 8574690039 | derivative of arctan u |  | 116 | |
| 8574690040 | derivative of arcsin u |  | 117 | |
| 8574690041 | Integration by parts |  | 118 | |
| 8574690042 | Limit definition of derivative with h | | 119 | |
| 8574690043 | Limit definition of derivative with delta x |  | 120 | |
| 8574690044 | Logistic differential |  | 121 | |
| 8574690045 | Logistics Equation |  | 122 | |
| 8574690046 | Elementary Series for e^x |  | 123 | |
| 8574690047 | Elementary Series for sin x |  | 124 | |
| 8574690048 | Elementary Series for cos x |  | 125 | |
| 8574690049 | Elementary Series for ln x |  | 126 | |
| 8574690050 | Taylor expansion |  | 127 | |
| 8574690051 | Euler's Method |  | 128 | |
| 8574690052 | Average Rate of Change |  | 129 | |
| 8574690053 | Inst. Rate of Change |  | 130 | |
| 8574690054 | Mean Value Theorem |  | 131 | |
| 8574690055 | Average Value of a Function |  | 132 | |
| 8574690056 | Intermediate Value Thm | A function f that is continuous on [a,b] takes on every y-value between f(a) and f(b) | 133 | |
| 8574690057 | Arc Length Cartesian |  | 134 | |
| 8574690058 | Arc Length Parametric |  | 135 | |
| 8574690059 | Arc Length Polar |  | 136 | |
| 8574690060 | Speed |  | 137 | |
| 8574690061 | Total Dist. | Check for turning points too! |  | 138 |
| 8574690062 | Polar Area |  | 139 | |
| 8574690063 | Parametric Derivatives |  | 140 | |
| 8574690064 | Polar Conversion for r^2 |  | 141 | |
| 8574690065 | Polar Conversion for x |  | 142 | |
| 8574690066 | Polar Conversion for y |  | 143 | |
| 8574690067 | Polar Conversion for theta |  | 144 | |
| 8574690068 | nth term test |  | 145 | |
| 8574690069 | Geometric series test |  | 146 | |
| 8574690070 | p-series test |  | 147 | |
| 8574690071 | Alternating series test | terms decrease in absolute value means convergence |  | 148 |
| 8574690072 | Integral test | Whatever integral does, series does | | 149 |
| 8574690073 | Ratio test | Also check each x value for IOC |  | 150 |
| 8574690074 | Direct comparison test |  | 151 | |
| 8574690075 | Limit comparison test |  | 152 |
