X is mapped to y f x the image of x under the function

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Unformatted text preview: f og the composite function of f and g lim f ( x) the limit of f ( x) as x tends to a dy dx the derivative of y with respect to x f ′( x ) the derivative of f ( x) with respect to x d2 y dx 2 the second derivative of y with respect to x f ″( x) the second derivative of f ( x) with respect to x ∫ y dx the indefinite integral of y with respect to x x →a ∫ b a y dx the definite integral of y with respect to x between the limits x = a and x=b ex exponential function of x log a x logarithm to the base a of x ln x the natural logarithm of x, log e x sin, cos, tan the circular functions A( x, y ) the point A in the plane with Cartesian coordinates x and y [ AB] the line segment with end points A and B 3 AB the length of [ AB] ( AB ) the line containing points A and B Â the angle at A ˆ CAB the angle between [CA ] and [ AB] ∆ABC the triangle whose vertices are A, B and C v the vector v → AB the vector represented in magnitude and direction by the directed line segment from A to B a the position vector OA i, j, k unit vectors in the directions of the Cartesian coordinate axes → the magnitude of a a → → | AB| the magnitude of AB v⋅w the scalar product of v and w A−1 the inverse of the non-singular matrix A AT the transpose of the matrix A det A the determinant of the square matrix A I the identity matrix P( A) probability of event A P( A′) probability of the event “not A ” P( A | B ) probability of the event A given B x1 , x2 , ... observations f1 , f 2 , ... frequencies with which the observations x1 , x2 , ... occur B ( n, p ) binomial distribution with parameters n and p N(µ ,σ 2 ) normal distribution with mean µ and variance σ 2 4 X ~ B(n, p ) the random variable X has a binomial distribution with parameters n and p X ~ N ( µ ,σ 2 ) the random variable X has a normal distribution with mean µ and variance σ 2 µ population mean k σ2 population variance, σ 2 = ∑ f (x − µ) i i =1 i n σ k , where n = ∑ f i i =1 population standard deviation x 2 sample mean k ∑ f (x − x ) i i 2 k , where n = ∑ f i 2 sn sn standard deviation of the sample Φ 2. 2 sample variance, sn = cumulative distribution function of the standardized normal variable with distribution N(0, 1) i =1 n i =1 Notation Of the various notations in use, the IBO has chosen to adopt a system of notation based on the recommendations of the International Organization for Standardization (ISO). This notation is used in the examination papers for this course without explanation. If forms of notation other than those listed in this guide are used on a particular examination paper, they are defined within the question in which they appear. Because students are required to recognize, though not necessarily use, IBO notation in examinations, it is recommended that teachers introduce students to this notation at the earliest opportunity. Students are not allowed access to information about this notation in the examinations. In a small number of cases, students may ne...
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This note was uploaded on 06/24/2013 for the course HISTORY exam taught by Professor Apple during the Fall '13 term at Berlin Brothersvalley Shs.

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