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9. (10 points) A certain gas satisfies the law where p=presure, V=volume, and T=temperature. Calculate and at the point where p=V=1 and T=2.

其他申論題

5. (10 points) Gauss' probability integral isEvaluate

6. (10 points) Determine and classify the stationary points of the function f(x,y)=xy+(x-y)3.

7. (10 points) Evaluate

8. (10 points) Evaluate ∫∫R xy dA , where R is the region bounded by and y=0, by converting to Polar Coordinates.

2. Find f'(2) if f(x)= and g(x) =

3. Trochoid x = 20 - sinθ, y = 2 - cosθ. Find the tangent line of the curve at θ = .

4. Trochoid x = 2θ - sinθ, y = 2 - cos θ. Find the area under the curve and above the x-axis for 0≤θ≤2π.

5. Let the region R be enclosed by the curves y = x2 and y = 2 -x2. Find the volume of the solid obtained by rotating the region R about x=1.

6. Let the region R be enclosed by the curves y = x2 and y = 2 - x2. Find the arc length of the region R.

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