Derivative of an integer
[DOC File]AP Calculus AB Syllabus
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Negative integer powers of x. Second and higher order derivatives. Velocity and Other Rates of Change. Instantaneous rates of change. Motion along a line (velocity, acceleration, free-fall, speed) Sensitivity to change. Derivatives in economics. Derivatives of Trigonometric Functions. Derivative of the sine function. Derivative of the cosine ...
[DOC File]Now the students are already familiar with derivative ...
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After evaluating g(h) for several small values of h, the students easily ascertain that the derivative of f(x) = 1/x is f’(x) = -1/x2. When this is written with a negative exponent, they also see, at least in this case, that the derivative rule developed for xn also holds when n is a negative integer.
[DOC File]Sums of Integer Powers--The Faulhaber Expansion
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The Bernoulli numbers may be defined by the recursion formula remaining after Sp(n) is removed from the derivative of the basic recursion formula. Here is a table of the first few Bernoulli numbers: B0 = 1. B1 = -1/2 . B2 = 1/6. B3 = 0. B4 = -1/30. B5 = 0. B6 = 1/42. B7 = 0. B8 = -1/30. B9 = 0. B10 = 5/66. B11 = 0. B12 = -691/2730. B13 = 0. B14 ...
[DOC File]AP CALCULUS AB
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If n is a positive integer, then Examples – Find the derivative. 1. 2. Let’s explore negative integer exponents… If . We can rewrite as , so use the power rule to find the derivative: How about fractional exponents? Find . We could also write as , so . Now we can generalize the power rule for any value of n.. The Power Rule (General Version)
[DOC File]A.P. Calculus Formulas
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A.P. Calculus Formulas 2008-2009. Hanford High School, Richland, Washington revised 8/25/08 1. floor function (def) Greatest integer that is less than or equal to x.
[DOC File]Calculus 1 Lecture Notes, Section 2.3
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Theorem 3.1: Derivative of a constant function. for any constant c. Proof: Let f(x) = c. Theorem 3.2: Derivative of f(x) = x. Proof: Let f(x) = x. Theorem 3.3: Power Rule (Derivative of a positive integer power function) for any integer n > 0. Proof: Let f(x) = xn. Theorem 3.4: General Power Rule (Derivative of any power function) for any real ...
[DOC File]Mathematical Statistics Review - Rice University
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For each integer n, the nth moment of X, , is . The nth central moment of X is . Mean = 1st moment of X. Variance = 2nd central moment of X. The moment generating function of X is . NOTE: The nth moment is equal to the nth derivative of the mgf evaluated at t=0. i.e. . Useful relationship: Binomial Formula is .
[DOC File]Chapter 3
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Derivative of f at . Standard: Alternate: 1. Consider the function where. a. Find the average rate of change in f on the interval [-1, 2] b. Using the standard definition of a derivative at … Find the instantaneous rate of change in f at (Precede your answer with Lagrange notation). c. Write an equation of the tangent line to the graph of at 2.
[DOC File]3 - James Madison University
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a. The derivative of a constant. b. The derivative of an identity function. c. The derivative of a linear function. d. The power rule for positive integer powers. e. The constant multiple rule. f. The sum rule. g. The difference rule. 2. When is a piecewise function differentiable? 3. Differentiate the following functions using and citing the ...
[DOC File]Solution of the Diffusion Equation
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Equation [10] can only be satisfied if the sine term is zero. This will be true only if xmax is an integral times . If n denotes an integer, we must have [11] We have an infinite number of solutions for X(x), as the integer n goes from 1 to infinity. We can write an individual solution as Xn(x) = sin(n x/xmax).
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