Part b: (**) We consider the function f(x, y) = x sin y - y cos x + X-R y Find fx(x, y), fxy(x, y), and fxyx (x, y).

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Q: 9. Solve the differential equation: xy + y'=100x

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A: We will use Ratio-Test to find convergence

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Q: What is the area of the region between y=x²-2x-3 and the x-axis from to 6? x=0

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A: The given differential equation is;  y''+3y'+2y=1/(7+ex).

Q: If z = -4xe³xy and x = √t, y = . Then, the value of dat t = 8 is equal to 3√2 (-1/2² + 2³/1) e + ² 4

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

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A: To find out the intervals on which the function is decreasing.

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A: Given: w=x2+y2, x=4t, y=5t and t=2.   Apply the Chain Rule; dwdt=∂w∂x·dxdt+∂w∂y·dydt    ...1

Q: 6. Σ(-1)n-1 sin (2) n=1

A: Explanation of the answer is as follows