7. (Integrals involving branches of multiple-valued functions) Show that (In a)? – (In b)2 2(а - b) In r J. (r+ a)(x + b) dr a, b > 0, a + b. [Hint: Integrate a branch of (log z)² (z+a)(z+b) around a keyhole contour.]

Q: 5. Show that the function h(x, y) defined by 1 if a? + y? 1 is discontinuous.

A: We can solve this using R.H.L ≠ R.H.L

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A: Disclaimer: Since you have posted a question with multiple sub-parts, we will solve the first three…

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Q: Please Provide Solutio, Thank you

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A: Given differential equation is y''' + y' = 0

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A: The solution of the problem is given in the next step.

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A: Exact differential equation and it's solution

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A: Exact differential equation, find the valued A and B.

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A: Given A,B,C,D We have to find values of parts then final answer.

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A: Solution :-

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A: Solve Legendre differential equation by series solution.

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A: We can solve this using given information

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Q: Estimate f(−1.99,−1.03) given that f(−2,−1)=−3, fx(−2,−1)=4, and fy(−2,−1)=1.

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