the graph Free Response Consider x² + 4y² + 6x – 8y + 9 = 0. of dy (a) Find dx (b) At which point(s) does the graph of the equation have a vertical tangent line? (c) At which point(s) does the graph of the equation have a horizontal tangent line?

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A: First find the first derivative at that given point than take the second derivative.

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A: To find the equation of the curve that passes through the point (0,0)

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A: What is the y(t) equation for the question marked ?

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A:

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A: The equation is exact as My=Nx, and the solution follows as:

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A: Given equation :

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A: To evaluate the below integral. ∫x=−∞∞∫y=0∞e−x2+y2dydx

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A:

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A: Detailed explanation mentioned below

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A:

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A: We will do this question by checking the conditions for the given options.

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A: Solution

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A: As per company guidelines we can solve first question. I hope that the given solution will help you.…

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A: Given, y=ex-πcscx We have to find y'.

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A: We can find dy/dx as below.

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A: Please refer the attached image for complete solution.

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

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Q: PART - B IA. Solve (4xy + 3y? - x)dx + x(x +2y)dy = 0 with y(2)=2. IB. Solve (x²D2 + xD - 1)y =ri

A: Since, you have posted multiple questions. As per guidelines we will solve only first question. If…