所屬科目：研究所、轉學考(插大)-高等微積分
1. Assume that sin x is continuous on R , prove that the function
3. (i) Let u = F ( x + g ( y)) . Find .
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 .
(ii) Given ， f ( x, t )dt , find F'( x ) , assuming suitable smoothness conditions on φ ,Ψ and f .
(i) → g pointwise on □ , where
(ii) does not converge uniformly to its limit on □ .
(iii) converges uniformly to its limit on [δ , ∞)
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.
. Prove that F' x=f( x) whenever f is continuous at x . 
， f ( x, t )dt , find F'( x ) , assuming suitable smoothness conditions on φ ,Ψ and f .
→ g pointwise on □ , where
does not converge uniformly to its limit on □ .
converges uniformly to its limit on [δ , ∞)