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Q: Use mathematical induction to prove that, for n ≥ 1, n³ – n is divisible by 3.
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A: one needs to simplify it.
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A: Since you have posted a multiple question according to guidelines I will solve first question…
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A: Since you have added more than one questions hence find the solution of the first one.
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Q: Find the coefficients an and bn of the Laurent series ∞ ∞ Σan(z-zo)" + [bn(z-zo)-n n=1 n=0 of the…
A: As per the question we are given the following function on complex domain : f(z) = z15 sin(1/z5) ,…
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A: We shall first split the integral into partial fractions and then use Cauchys integral formula
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A: Functions :PolynomialRationalExponentialLogarithmicSinusoidal and other trigonometric functions.
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A: Given that, Give the 7) Law of cosines 8) Heron's formula 9) Cofunctions
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A: Mathematical Description of GRADIENT: In vector calculus, the gradient of a scalar valued…
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A: In octal subtraction the carry is '8' (Like we do in decimal system carry as '10')
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A: Here, A=3137077468328491, B=45675678678978910. To Find: BA.
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A: Since you have posted a multiple question according to guideline I will solve first(Q1) question…
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Q: 5. For all matrices, when the product is valid, we have A(B+C) = AB + AC
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A: Four terms :1) Dependent variable2) Independent variable3) Predictor variable4) Explanatory variable
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Q: Gamma and Beta Functions 4 (-) fo {√4x in (√x))³dxamScanner (6) dx 4x-x²
A: ∫04dx4x-x23=∫04dx4x-x213=∫04dx(4x)131-x413 =1413∫04(x)-131-x413dx , put…
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A: I have explained everything with in the solution, please go through that.
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Q: Use Variation of Parameters to find a particular solution to y" +9y = tan (3x).
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Q: 100 Σ (3* + 2k - 1) k=1
A: ∑k=11003k+2k-1
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Q: mplify. Write your answer in polar form. п 57). √₂(cos 5 п COS - 4 4 2 cos 5 п 4 + isin + isin 5T 4
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Q: Using De Moivre's Theorem prove the following: tan(50) = 5 tan(0)-10 tan³ (0) + tan5(9) 1-10…
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Q: 1 Let P = -3 -5 4 6 -7 H10 2 2-1 - 8 = 4₂ 43 = V₂ = 5, and V33 4 Complete parts (a) and (b). = 6 a.…
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Q: the positive solutions of the rational difference equation aSn-q+bSn-r+cSn-s Sn+1 = Sn-pdSn-q +…
A: As per the question, we are given a specific form of a difference equation and are tasked with…
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