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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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其他申論題
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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5.
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6.
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7. Calculate ∫(x3+x)5(3x2+1)dx
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9. Calculate ∫ sec 2(5x+1)∙ 5dx
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10.
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1. Please solve the differential equation (20%) (x2 +2xy-y2)dx+(y2 +2xy-x2)dy
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2. Solve the following differential equation with zero initial condition. (20%) t2y"(t)-2ty'(t)+2y(t)= cos(2ln(t)), t＞0
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3. Solve the following differential equation (10%) xy" -4y' = x
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4. Find the value of by solving the initial value problem for the given system of differential equations, where H(t-a) is unit step function or Heaviside function. Show the details. (20%)
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