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研究所、轉學考(插大)-微積分
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112年 - 112 國立臺灣大學_碩士班招生考試題：微積分(D)#130254
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(5) The 4th nonzero term of the Maclaurin series of the function f(x) = √(9 + x²) is
(5)
.
其他申論題
(1) Evaluate = (1) .
#552088
(2) Let y = f(x) be a function defined implicitly by the equation 2(x² + y²)² = 25(x² - y²) near x = 3, y = 1. By linear approximation f(2.87) ≈ (2) .
#552089
(3) Let R be the region described by {(x, y) | cos x ≤ y ≤ sec²x, 0 ≤ x ≤ }. The volume obtained by rotating R about the y-axis is (3) .
#552090
(4) The area of the region inside the polar curve r = 5 + 3 cos θ is (4) .
#552091
(6) The coefficient of in the Maclaurin series of g(x) = is (6) .
#552093
(7) The tangent plane of the surface xy²z³ = 8 at the point (2, 2, 1) is given by the equation (7) = 0.
#552094
(8) Evaluate cos(y5) dy dx = (8) .
#552095
(9) Evaluate dx dy = (9) .
#552096
(10) Let E be a solid in the first octant. The largest possible value of (9 - x² - y² - z²) dV is (10) .
#552097
(11) Sketch the curve y = and its asymptotes. Find the intervals of increase/decrease and concavity. Label local extrema and inflection points if any.
#552098
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