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研究所、轉學考(插大)-微積分
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109年 - 109 國立臺灣大學轉學生招生考試試題_理工科聯招：微積分(B)#110852
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題組內容
1.
(c)
=___(3)____.
其他申論題
5. (12 pts) Solve the integral equation
#474770
6. (14 pts) Let f :R→ R be a differentiable function. Suppose that 0 ≤ f' (x) ≤ f(x) for all c . Show that g (x) = is decreasing. If f vanishes at some point, conclude that f is identically zero.
#474771
(a)=__(1)__ , where [x] is the greatest integer which is less than or equal to x.
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(b) =__(2)__，where a, b are constants and ab ≠ 0.
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(a)=__(4)__.
#474775
(b) x3 -y2+y3 =x. At (x, y) = (0, 1).=__(5)__
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(c) f(x，y，z)==__(6)__.
#474777
(d) f(x,y)= for (x,y)≠(0,0) and f(0,0) = 0. The directional derivative of f along u = (cosθ,sinθ) at (0,0) is__(7)__.
#474778
(a) Choose correct statement(a) about. g(x): __(8)__ i. g(x) is discountinuous at x = 3.ii. g(x) is not differentiable at x = 3.iii. g(x) is differentiable at x = 0 and g'(0) = -1.iv. g(x) ＜ 0for -1 ≤x≤0.
#474779
(b) The local minimum values of g(x) occur at x =__(9)__
#474782
=___(3)____.
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=___(3)____.