Limit of f x as x tends to a dy dx the derivative of y

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Unformatted text preview: 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 8 sin, cos, tan the circular functions arcsin, arccos arctan the inverse circular functions csc, sec, cot the reciprocal 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 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 v×w the vector 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 9 x1 , x2 , ... observations f1 , f 2 , ... frequencies with which the observations x1 , x2 , ... occur Px probability distribution function P(X = x) of the discrete random variable X f(x) probability density function of the continuous random variable X F(x) cumulative distribution function of the continuous random variable X E(x) the expected value of the random variable X Var(X) the variance of the random variable X µ population mean k σ 2 population variance, σ = ∑ f (x − µ) i i =1 2 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 2 sample variance, sn = sn standard deviation of the sample 2 s n −1 unbiased estimate of the population variance, i =1 n k 2 s n −1 = n = n −1 ∑ f (x i i − x) 2 i =1 n −1 i =1 k , where n = ∑ f i i =1 B ( n, p ) binomial distribution with parameters n and p Po(m) Poisson distribution with mean m N(µ ,σ 2 ) normal distribution with mean µ and variance σ 2 X ~ B(n, p ) the random variable X has a binomial distribution with parameters n and p X ~ Po(m) the random variable X has a Poisson distribution with mean m X ~ N ( µ ,σ 2 ) the random variable X has a normal distribution with mean µ and variance σ 2 Φ cumulative distribution function of the standardized normal variable with distribution N(0, 1) 10 ν number of degrees of freedom χ2 chi-squared distribution χ the chi-squared test statistic, where χ 2 calc 2 calc = ∑ ( fo − fe )2 fe A\B the difference of the sets A and B (that is, A \ B = A ∩ B′ = {xx ∈A and x ∉ B}) A∆ B the symmetric difference of the sets A and B (that is, A∆B = (A \ B) ∪ (B \ A)) κn a complete graph with n vert...
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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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