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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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(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
其他申論題
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
#447882
2. (i) State Mean Value Theorem. .
#447883
(ii) Prove that the function f ( x) = sin x is uniformly continuous on
#447884
3. (i) Let u = F ( x + g ( y)) . Find .
#447885
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 .
#447887
(ii) Given ， f ( x, t )dt , find F'( x ) , assuming suitable smoothness conditions on φ ,Ψ and f .
#447888
(i) → g pointwise on □ , where
#447889
(ii) does not converge uniformly to its limit on □ .
#447890
(iii) converges uniformly to its limit on [δ , ∞)
#447891
(a)
#447892
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