Confirm that the Integral Test can be applied to the series. Then use the Integral Test to determine the convergence or divergence of the series. Σ e-n n = 1 e-X dx = O converges O diverges

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A: here we have to find the volume.

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A: Divide the polynomial by x+2 and simplify it.

Q: Find the 5th roots of 9. -16/2 + 16vZi

A: =12+32i9De Moivre's theorem;=cosπ3+i sinπ39= eiπ39=ei3π=cos3π + isin3π=-1

Q: 00 1 25. nº – 7 n=1 00 .3 IM:

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A: I am attaching image so that you understand each and every step.

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A: (-1)1/2= i

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A: Given: Complex number 6+5i

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Q: Evaluate the integral 1 12 3x (x - 1) dx 0.

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Q: H.Evaluate the triple inteqral. 8zdV E where E is bounded by the cylindter 4 + 2? = 9 and 2-0 and…

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A: We can determine the length of the curve as below.

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Q: 1. find af/ax andaf/ay .. ) (x. y) = Vx² + y

A: As per guidelines we can answer only one question at a time, so if you need more answer kindly…

Q: 2. -2 +1- 16 + +

A: Given  (2)

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A: Given the Bernoulli's differential equation is dydx - yx = y9

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A: For the solution of the problem follow the next step.

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A: topic - exponential function

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Q: Example 4 Identify and sketch the curve 153x-192xy +97y2 - 30x- 40y – 200 = 0 !!

A: Given:     153x2-192xy+97y2-30x-40y-200=0  We have A=153, B=-192, C=97 So, cot2θ=A-CB=153-97-192…

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Q: Q\ use Euler's method to the differen fial equa tion Solve y=XVXY When y co) =\ cnd

A: For the solution follow the next step.

Q: Let f(x) = 2x + 3/3x-2 , g(x) = 4x/3x − 2, h(x) = √3x − 12, F(x) = 3x + 4, G(x) = 2x − 3 a) Find the…

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Q: 13. ап V21+3п 15. ат — 2" cos пл

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Q: Function Factors f(x) = 2x3 + x2 – 5x + 2 (x + 2), (x – 1) (a) Verify the given factors of f(x). (x…

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