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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
(b)
dx.
其他申論題
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)
#527594
(b)
#527595
(a) x sec²x 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.
#527598
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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8. (10 points) Find (f⁻¹)'(5) forf(x) = x⁵ + 2x³ + 2x.
#527604
dx.
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dx.