Use mathematical induction to prove that n³ - n is divisible by 3, for every positive integer n.

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Q: 5. Evaluate the following integrals: (a) *³ ** cos(x) dx dy 4y -x²-y² (b) √ √ ² dy dx (Hint: Use…

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Q: 10- 5 -5 -10 5 10 -10- This is the set of points such that |z| = |z − zº| for some zº € C. . Enter…

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Q: 5. Find the Solution: y" + 2y' + y = cost y π y (²₁7) = 1 y' y'(-7)= = 2

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Q: Q))Solve the Recurrence relation Xk+2 + Xk+1 - 6xk = 2k-1 where xo = 0 and x₁ = 0

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Q: 32. Evaluate: lim X18 10 (x + 1)¹⁰ + (x + 2)¹0 + 10 X + (x + 2012) ¹0 ... + 2012¹0

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Q: 2. Solve the yk+2+9yk = 4k + cos 3k using method of undetermined coef- ficients.

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Q: the matrix has two eigen vector one of (ارفق الاجابة)this N|HN|W 0 1 2 0 }] -1 0 12032

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Q: 5. Evaluate the following integrals: cos(x) dx dy 4y -1²-y² (b) ff 2-y² dy dx (Hint: Use polar…

A: Some of the properties of integration  ∫cosx dx=-sinx+C∫f(g(x))g'(x)dx=∫f(t)dt∫eaxdx=eaxa+C