| 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 |