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7. (10 points)Find the interval of convergence of the series. Then identify the values of x for which the series converges absolutely or conditionally.

其他申論題

3. (10 points)If , find the partial derivatives

4. (10 points)Evaluate

5. (10 points)Find the derivative of the function simplify where possible.

6. (10 points)Find the area of the polar region R, where R is bounded by the smaller loop of the curve r = 1 + 2cosθ.

8. (10 points)In which direction from the point (1,1) is the directional derivative of f(x)=x2+y2 zero?

9. (10 points)Determine and classify the stationary points of the function f(x,y)=x2+y3+6xy-7x-6y.

3.It is known that 2x3+y2= 5xy. Determine the value of dy/dx when (x,y)=(1,2). (10%)

4. Find the arc length determined by the curve y= over 1≤ x＜ 2. (10%)

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