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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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4. (10 points) Evaluate
|
(2,0)
for
u(x,y) = h(x² + y², 3x – 4y)
where
h(s,t) =
其他申論題
(b)
#527595
(a) x sec²x dx.
#527596
(b)dx.
#527597
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
5. (10 points) Find the volume of the solid generated by rotating the curvey = sin(x²)over 0 ≤ x ≤ 1 around the y-axis.
#527600
6. (10 points) Evaluate the infinite sumby some manipulations of the Taylor series of f(x) = xeˣ.
#527601
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.
#527602
8. (10 points) Find (f⁻¹)'(5) forf(x) = x⁵ + 2x³ + 2x.
#527604
9. (10 points) Evaluatedydx.
#527605
10. (10 points) Use Lagrange multiplier to find the extreme value off(x, y, z) = exyzsubject to the constraintx³ - y² + z³ = 24.Also, indicate the value(s) you obtain is (are) maximum or minimum.
#527606
|(2,0) for
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|(2,0) for