1.(15%) Find the local maximum and minimum values and saddle  points  of the function f(x,y)=e^y(y²-x²).

2. Given the following plot of oxygen binding versus pressure of O2 for myoglobin and hemoglobin at pH 7.2, (1) draw a curve that shows what happens when the pH is increased to about 7.6 and (2) draw a curve that shows what happens when the pH is decreased to about 6.8. (3) What is the pH value at which hemoglobin has higher affinity of O2? Please provide the explanation from the curves. (10%)

3. β-oxidation: (1) Please plot the 4 steps of β -oxidation reaction and label the enzyme and the involved energy molecules of each step (10%). (2) Please determine the number of ATP equivalents if we complete β -oxidation of a palmitic acid (C18:0) to CO2 and H2O. By the calculation, how many kJ can be generated by 1g palmitic acid if the molecular weight of B-linolenic acid is 256 Da? (Assume for the calculation that NADPH is worth 3.5 ATPs, NADH is 2.5 ATPs, FADH2 is 1.5 ATPs and one Acetyl- CoA produces 10 ATPs and the bydrolytic energy of ATP is 31 kJ/mol) (10%).

4.How many NADH, FADH2 and GTP can be generated for one molecule of acetyl-CoA passing through TCA cycle? How many ATP can be produced if these NADH, FADH2 and GTP passing through electric transfer system? (10%)

5. What is the start building block of cholesterol? What is the control enzyme for cholesterol biosynthesis? What is the major transporter of cholesterol in circulation system? How the cells manipulate the oversupply of cholesterol? (10%)

2. (10%) The length width w, and height h of a box change with time. At a certain instant the dimensions are = 1m and w= h= 2 m, and and ware increasing at a rate of 2 m/s while h is decreasing at a rate of 3 m/s. At that instant find the rates at which the length of a diagonal are changing. (The length of diagonal L =)

3.(25%) Sketch the graphs of (You need to describe A: domain; B: intercepts; C: asymptotes(horizontal and vertical if any); D: intervals of increase and decrease; E: local maximum and minimum values; F: interval of concavity; G: point of inflection; H: sketch the curve)

(a)

(b)

(c)

5.(20%) Given the series ,(a) find the series' radius and interval of convergence. For what values of x does the series converge (b) absolutely,(c) conditionally?