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112年 - 112 國立政治大學_碩士班暨碩士在職專班招生考試試題_統計學系:基礎數學#130257
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2. Use ε-δ argument to show that
= 0.
其他申論題
(12) Evaluate the definite integral xln ln(x² - 4x + 5) dx.
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(13) A logistic population model with relative growth rate 0.1 per year and carrying capacity 50 thousand can be expressed by the differential equation =0.1P(1 - ), with P in thousands and t in years. Given that the initial population is 9 thousand. Find the population size after 20 years. (If you memorized the formula, then you need to derive it for this problem.)
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(14) Find the extreme values of f(x, y, z) = z subject to the constraints x² + y² = z² and x + 2y + z = (16)
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(a)
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(b)
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(c)
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(d)
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(e) ∫ sin5x cos2 xdx.
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4. Find if tan= x + y.
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