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研究所、轉學考(插大)-微積分
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109年 - 109 台灣綜合大學系統_學士班轉學考聯合招生考試:微積分B#124117
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題組內容
2. (10 points) Evaluate the following integrals
(a)
x sec²x dx.
其他申論題
第貳部分:作文題Our emotional, psychological, and social well-being is all part of our mental health. At every stage of life, mental health is important because it affects how we think, feel, and act as we deal with life.Please compose a 300-word essay discussing effective approaches for university students to maintain mental wellness.
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IV. CompositionIt has been suggested, "education should be regarded as the means by which the inequalities among individuals are to be erased and by which every desirable end is to be achieved." Use the preceding quote as the main idea to develop an article of approximately 300 words and make sure you provide a title for your essay.
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(a)
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(b)
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(b)dx.
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3. (10 points) Evaluate |(0,1) foru(x,y) = (eˣ - dt.Note: Answer must in numerical expression and natural constants like π, e, ...etc.
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4. (10 points) Evaluate |(2,0) foru(x,y) = h(x² + y², 3x – 4y)whereh(s,t) =
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5. (10 points) Find the volume of the solid generated by rotating the curvey = sin(x²)over 0 ≤ x ≤ 1 around the y-axis.
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6. (10 points) Evaluate the infinite sumby some manipulations of the Taylor series of f(x) = xeˣ.
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7. (10 points) A dog is running along a semi-circular track with radius 1 km incounterclockwise direction with speed 0.1 km per minute (See Figure).Let h be the distance between the dog and point A. Find the rate of change of h at point D, half way between B and C.
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