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研究所、轉學考(插大)-微積分
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104年 - 104 國立臺灣師範大學_轉學生招生考試試題_數學系二年級：微積分#118784
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7. Explain the fundamental theorem of calculus (two parts in this theorem), no proof is needed. (10 points)
其他申論題
3. Find the interval of convergence for the series (10 points)
#506417
4. Find all local maxima, local minima, and saddle points of the function f(x,y)=x3+3xy+y3. (15 points)
#506418
5. Find the absolute maxima and absolute minima of the function g(x,y)=x2+xy+y2-6x on the rectangular plate O≤x≤5,-3≤y≤3. (15 points)
#506419
6. Let C be a curve which is the intersection of two surfaces x2+y2=8 and x +z = 3. Find the tangent line to the curve C at the point P(2,2,1) . (10 points)
#506420
(A) What is the pI for the following peptide: Ala-Glu-Val-Asp-Lys-Leu? (6%)
#506422
(B) What is the C-terminal amino acid in this peptide? (3%)
#506423
2. If an enzyme-catalyzed reaction with a KM of 3.5 mM has a velocity of 5 mM/min at a substrate concentration of 0.5 mM, what is the Vmax? (6 %)
#506424
3. This is a cycle of the B-oxidation of saturation fatty acid. Please calculate how many ATP can be generated in a complete oxidation of Myristic-CoA (C14:0-CoA) (if you consider one NADH produces 2,5 ATP, one FADH2 produces 1.5 ATP and one Acetyl-CoA produces 10 ATP)? (10%)
#506425
4. Please explain the mechanism of how F1F0-ATPase produces ATP in mitochondria. You need include the teams of proton gradient, c subunit of F0, and a and B subunits ofF1.(5%)
#506426
5. Please draw a potential energy diagram for the exothermic reaction A→B and explain why the enzyme-catalyzed reaction is faster than the uncatalyzed reaction. (10%)
#506427
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