8. Given, h(x) =2 – x and g(x) = -x² + 4 a) Plot the two functions on the same graph for -2 < x <4 b) Calculate the area between the curves of h(x) and g(x) for -2

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A: Topic = Area

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A: NOTE-Since you have asked multiple question, we will solve the first question for you. If youwant…

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A: f(x)=ex-3x Take derivative wrt to x f'(x)= ex-3

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A: answer is in next step

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A: We will find the cross product and area.

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A: Solution: here we use the range formula

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Q: 9. Determine by the root test if Ln=2 (4n-5\n 2n+1, converges or diverges.

A: Explained below

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A: We will solve the problems.

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Q: 9. sin ở In(cos 0) de

A: let I=∫sin θ ln(cosθ) dθ Integration By parts: ∫udu=uv-∫vdu u=ln( cosθ) ; du=1 cosθ-sinθdθ=-tanθdθ…

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A: We can solve as follows

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A: The region bounded by the curves y=x3, y=x+6 &amp; 2y+2=0 is: