Show that 8 1 - sin x x² 1 -dx converges.

Q: Let ƒ(x) = (x³ + 4x + 6) ³ f'(x) = 9x¹ + 12x² f'(1) = 2541 X OF

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Q: f(x) = e^-1/x^2 show that there is no positive number M such that each natural no n, |f^n(x)|<…

A: We need to prove that there is no positive number M such that each natural number n,

Q: If an initial amount Ao of money is invested at interest rate i compounded n times a year, the value…

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Q: Determine if  ∫3-2(1/x^3)dx  is convergent or divergent.

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Q: Does sin () x 7 converge or diverge? Why?

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Q: Let 6х — 8 - f(x) = ln 5x + 4 f' (x) =

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Q: 10) Calculate a lower sum for f(x) = 2x + 5 over the interval [0, 2] using 4 rectangles. %3D

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Q: The graph of f is shown in the figure. 6. 4 х 14 -4 -6+ 2-

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Q: Expand f(x) = (1+x)^1/2 to the linear order of x and estimate the error when 0<x<1/2.

A: Step 1:Step 2: Step 3: Step 4:

Q: Use a comparison test to determine whether I (ln(x) — 1) dx converges or diverges.

A: (i) If f(x)≤g(x),∀x∈[a,∞) and ∫a∞g(x)dx is convergent,  then ∫a∞f(x)dx is convergent. (ii) If…

Q: Find the x>0 which minimizes 2*. Round to one decimal

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