For the next three questions, consider the following differential equation: (2y sin r cos r-y + 2y²e™v° )dx – (x – sin²r – 4 4rye)dy = 0 Let M be the cocfficient of dr and N be the coefficient of dy. 13. 14. 15.

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

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A: Given:M(x,y)dx+(x2+x)dy=0

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A: To find the volume.

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Q: 9. 10. 10+ 12-10

A: Topic:- function   

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A: Solution: ∫-3dy2y2+14y+70 Take out the common -32∫1y2+7y+35dy

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A: The given integral,           ∫015238-38x2dx

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A: ∫cotx-cscx2 dx

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A: The objective is to find the limit of the above function at x equal to 0.

Q: e" corh w dw

A: Explained below 

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

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Q: dx Ied x+l

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A: ∫1tdt=lnt+C

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Q: 11. Verify that the conclusion of Clairaut's Theorem holds for the function: f(x, y) = exy sin(y)

A: The objective is to verify the conclusion of clairaut's theorm.

Q: x-1 6. f(x)= x +3x 4x 7. f(x)=-- x +4 8. f(x)=- x +6x+9 9. f(x)=-- x +1 L0. f(x) = x' + 4x + 4x + 2

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Q: n

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A: Topic :- derivatives  Note:- as per our guideline if more than one question uploaded than only first...

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Q: 2. An iPhone 13 pro max is dropped from the top of the Balayong Park monument, 225 ft high. (a) How ...

A: This question can be solved by using the equations of motion.

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