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110年 - 110 國立台灣海洋大學_碩士班招生考試_運輸科學系碩士班不分組：微積分#103781
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4. Find the eigenvalues and eigenfunctions of the following problem. (20%) y"+λy=0；y'(0)=y'(L)=0
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5. Determine the inverse Laplace transform of the function. (15%)
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6. Let vectorfield F=2yzi-4xzjtspk. Evaluate the value of the surface integral , where Σis the sphere of radius 5 about (-1,3,1) . (15%)
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For problem 1~10, each counts 10 points 1.
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3.
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4. Please prove the quotient rule: If f and g are differentiable at x and g(x)≠0, then the quotient f /g is differentiable at x and
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7. Calculate ∫(x3+x)5(3x2+1)dx
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8.
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