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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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4. Find all local maxima, local minima, and saddle points of the function f(x,y)=x
3
+3xy+y
3
. (15 points)
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(3) ∫cos(2θ)cos(3θ)dθ (7 points)
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(4) (8 points)
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2. Evaluate or explain the limit does not exist. (10 points)
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3. Find the interval of convergence for the series (10 points)
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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
7. Explain the fundamental theorem of calculus (two parts in this theorem), no proof is needed. (10 points)
#506421
(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
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