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2. (8 points) Find an equation of the tangent line to the graph of x sin 2y = y cos 2x at the point.

其他申論題

7.(8 points)Find the value of ∂z/∂x at point (1, 1, 1) if the equation xy + z³x - 2yz = 0 defines z as a function of the two independent variables x and y and the partial derivative exists.

8.(12 points)Find the absolute maximum and minimum values of f(x, y) = 2 + 2x + 2y - x² - y² on the triangular plate in the first quadrant bounded by lines x = 0, y = 0, y = 9 - x.

4. (8 points) Let . Find (f-1)'(0).

5. (12 points) Consider the function given by f(x) = Find the interval of convergence for f(x).

6. (12 points) Find all local maxima, local minima, and saddle points of the function f(x, y) = 2x3 + 3xy + 2y3.

7. (12 points) Evaluate the double integral dA where R is the square with vertices (0,1), (1,0), (2,1), (1,2).

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