MATH 2D

Final - Practice 2 | General | Gorodetski

1. Find the equation of the plane through the line of intersection of the planes $x - z = 1$ and $y + 2z = 3$ and perepndicular to the plane $x + y - 2z = 1$.

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2. Find the curvature of the ellipse $x = 3\cos t, y = 4\sin t$ at the points $(3, 0)$ and $(0, 4)$.

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3. Find the absolute maximum and minimum values of the function $f(x, y) = 4xy^ - x^2y^2 - xy^3$ on the set $D = \{ (x, y) | x \ge 0, y \ge 0, x + y \le 6 \}$.

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4. Find the volume of the solid above the paraboloid $z = x^2 + y^2$ and below the half-cone $z = \sqrt{x^2 + y^2}$.

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5. Evaluate $\int_0^3 \int_{-\sqrt{9 - x^2}}^{9 - x^2} (x^2 + y^2 + \sin(\pi(x^2 + y^2))) dy \; dx$

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