3. Let u = f(x, y), x = r cos 0 and y = r sin 0. Show that: 1 1 Urr + −Ur + - U00 = Uxx + Uyy. p2 r

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Q: 13. Convert the rectangular equation to polar form. 1+1=2

A: x2 + y2 = 25 is compare with r2cos2θ + r2sin2θ = r2 so here r = 5 tanθ = x/y tanθ= 1 θ= π/4 so the…

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A: SOLUTION-

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A: Since you have asked multiple questions,we will solve the first question for you . If you want any…

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A: Integrate the given series expansion of f term-by-term from zero to x to obtain the corresponding…

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A: Given query is to find the phase shift.

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A: We can solve this as follows:

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A:

Q: Q.3) Evaluate the following dx 1) [ x² + 10x + 30 T 2) [²√³x² 3) ² ² 1/2 dx xy y sin x dx dy dx dy

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A: Solution

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A: Given Function f f(x,y)=14-x2-y2 on line x+2y=5We need to find the maximum value For the line…

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A: Please see the below picture for detailed solution.

Q: 6) Write an equation of the plane through the points P(5,3,8), Q(6,4,9), and R(3,3,3).

A: The plane passing through the points P5,3,8, Q6,4,9 and R3,3,3

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Q: 8. Find the antiderivative of (12x²)ex³ O 4e+³ 4eX +C O (4x³)e+³ +C O None of these Cannot be found

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

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A: