A. Show, or argue numerically, that the equation has precisely one positive root. B. Determine the positive root with a precision of at least 8 decimals

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A: in this problem we use some formula for finding the coefficients of  Fourier series .

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A: To Explain: what type of nodes do we choose to avoid the Runge phenomenon?

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A: Given : i ex , e-xand e2x            : ii 1 , ex+e-x and ex-e-x To Prove : Given function h…

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A: It seems 2nd image is partial. We answer accordingly.

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Q: 21.) Evaluate. [₁²x(x² - 1)² dx -1)7

A: We can solve this by substituting the veriable x^2-1 as u

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Q: 8.) Double declining balance depreciation. An office machine is purchased for $5200. Assume that its…

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A: Definition of function is given below

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A: To Explain: The formula for Quasi-Newton method.

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A: I have given the answer in the next step. Hope you understand that

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A: We have to prove that if f(n) is multiplicative, then f(n)n is also a multiplicative function.

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A: Given: L.H.S.=c(n, n-2)R.H.S.=2n3+3n4To prove:  L.H.S.=R.H.S.

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