4. Find the Laurent series of the following function : f (z) = (z + 1)(z + 3) 1 region 2 < |z – 1| < 4 nt

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A: Formula:ddx(a f(x))=a  ddxf(x)ddx(xn)=n xn-11)f(x)=10 x10f'(x)=10 ddx x10f'(x)=10 10 x10-1f'(x)=100…

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A:

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A: To evaluate the given integral.∫3-16x-12 dx

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A: To find the radius of convergence we will find first limn→∞an+1anthen equate it to less than 1

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A:

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A: Solution is given below:

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A: answer is in next step

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A: Let's find.

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A:

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A: Explanation of the answer is as follows

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A: Solving

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A:

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A: Follow the procedure given below.

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A: We have to find the area using left and right endpoints.

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A:

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A:

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A: This question can be solved using the concept of root test.

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A:

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A: Here we have to find the integration.