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研究所、轉學考(插大)-微積分
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93年 - 93 國立暨南大學轉學生招生考試試題_微積分_(資工系)#125297
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1.Find
[Hint: limit of Riemann sums]
其他申論題
(a) Find the angular acceleration of the pulley.
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(b) Assuming that the system starts from rest, find the speed of m₁ after it has fallen by H.
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(a) What is the energy of the photon emitted as a result of the transition?
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(b) What are the higher quantum number and lower quantum number of the transition producing this emission?
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2.(a) Show that If f is continuous on [a,b] and c is any number in [a,b], then the function F(x) = f(t)dt is continuous on [a,b], differentiable on (a,b), and satisfies F'(x) = f(x) for all x in (a,b). (Hint: f(t)dt = f(t)dt + f(t)dt )
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(b)f(t)dt = √(3x²+1) - 5 , find f(x).
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3. If the circle x²+(y-b)² = a², b＞a＞0, is rotated around the x-axis, the resulting "doughnut-shaped" solid is called a torus. Find the formula for the volume of the torus.
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4. (a)Prove that f(x)dx = f(a-x)dx
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(b)By (a), evaluate
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(a)Show that it is increasing.
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