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研究所、轉學考(插大)-高等微積分
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107年 - 107 東吳大學_暑假轉學生招生考試_數學系三年級：高等微積分#105419
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2. (i) State Mean Value Theorem. .
其他申論題
4.《花間集
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5.《劍南詩稿》
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四、作文(文言或白話不拘) 題目:創意與傳統
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1. Assume that sin x is continuous on R , prove that the function is continuous on ( -∞,0) and (0, ∞) , discontinuous at 0 , and neither f (0+ ) nor f (0- ) exists
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(ii) Prove that the function f ( x) = sin x is uniformly continuous on
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3. (i) Let u = F ( x + g ( y)) . Find .
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(ii) Find all the critical points of the function f ( x, y ) = x 2 + 3 y 4 + 4 y 3 + 12 y 2 and tell whether it is a local maximum, local minimum, or a saddle point. x
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4. (i) Let f be integrable on [a, b] . For x ∈[a, b] , let . Prove that F' x=f( x) whenever f is continuous at x .
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(ii) Given ， f ( x, t )dt , find F'( x ) , assuming suitable smoothness conditions on φ ,Ψ and f .
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(i) → g pointwise on □ , where
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