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Multinomial Theorem
2021-10-20
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This theorem is the generalization of Binomial Theorem. Binomial Theorem states that the coefficient of $x_{1} […]

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Binomial Theorem
2021-10-19
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This theorem is the generalization of $(x+y),\ (x+y)^{2},\ (x+y)^{3},\cdots$, and states that the coefficient […]

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Euler’s Formula
2021-10-16
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Notice that lie on the circle of radius 1 rotated by angle in the complex plane as shown in figure, and Euler& […]

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De Moivre’s Theorem
2021-10-15
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The th root of a complex number can be calculated by expressing the complex number in polar form and using De […]

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Roots of a Complex Number
2021-10-14
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The solution of is called the th roots of a complex number . All points, , lie on the circle of radius , and a […]

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Proof of Lim sin x/x =1
2021-08-16
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Proof : We use a geometric argument to prove the limit value. We first prove that the right limit value is equ […]

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Important Limit Values
2021-08-16
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Trigonometric Functions In the limit of the indeterminate form of trigonometric functions, the principle is to […]

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Moment Generating Functions
2021-08-04
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The moment generating function of X is defined by $$M_{X}(t)=E[\rm{e}^{Xt}]$$ where is the expectation. Since […]

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Quadratic Functions
2021-08-03
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A quadratic function is a polynomial of degree 2 which has the form $$f(x)=ax^{2}+bx+c$$ where is an unknown a […]

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General Leibniz rule
2021-08-01
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Notice that is the binomial coefficient and denotes the th derivative of , and in particular . th derivative n […]

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