MAT 1300 Review Questions 3 Summer 2022
Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: daixieit
Review Questions 3
MAT 1300, Summer 2022
1. 
4 x
2. j 
x dx .
3. j1 
dx .
4. Consider functionsf (x) = x2 – x − 4 and g(x) = −2x2 + 5x + 5.
(a) Find the area of the region under the graph of g(x) and above the graph off (x). (b) Find the area of the region between the graphs off (x) and g(x) in interval [2, 4].
5. Suppose the demand function and the supply function are p = D(q) and p = S(q), respectively, where D(q) = 13 − 2 
, and S(q) = 4 + 
. Find the consumer's surplus and the producer's surplus.
6. Find the average value of the function y = 
in interval [2, 4].
7. Suppose a person borrows $120,000 from a mortgage company with annual interest rate 3. 15%. The amortization period is 25 years. Assume the payment is a continuous stream with a constant density. What is the monthly payment?
8. Suppose I am planning to deposit 5 thousand dollars a year in to a bank account with annual interest rate 4% to prepare for the university expenses of my new born child. Assume my payment is a continuous stream, and the interest is compounded continuously. What is the future value of this stream after 18 years?
9. Use the definition of improper integrals to determine whether each of the following improper integral is convergent or divergent. If it is convergent, find its value.
x
(b) j1 (x2 一 1)2 / 3 dx .
10. Letf (x, y) = 
2x1一 3y . Find the first and second order partial derivatives.
11. Find all critical points of the function z = x2y + 2xy2 – 2x2 + 6xy, and use the second derivative test to determine, for each of the critical point, whether function z(x, y) attains a local minimum, or a local maximum at this point, or the graph of z(x, y) has a saddle point at this point.
2022-07-14