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1. Find the radius of convergence and interval of convergence for the given power series. (5 分)

其他申論題

a. What is the domain of R? (5 points)

b. How many databases were present when DataCorp began the transfer? (5 points)

c. How many databases still needed to be transferred in 2009? (5 points)

8. A manufacturer can produce printer paper at a cost of $2 per ream. The paper has been selling for $5 per ream, and at that price consumers have been buying 4,000 reams per month. The manufacturer is planning to raise the price of the paper and estimates that for each $1 increase in the price, 400 fewer reams will be sold each month. What price corresponds to the maximum profit? (10 points)

2. Consider the function . Find f'(x). (5 分)

3. Differentiate x² log₁₀(2x²+3). (5 分)

4. Approximate cosx by a fourth-degree polynomial for values of x close to 0. (5 分)

5. A wire of given length L may be cut into pieces to form a square and an equilateral triangle. How should it be cut if the sum of the areas of the square and the equilateral triangle is to be a minimum? A maximum? (10 分)

6. What is the maximum directional derivative of the function f(x, y) = 75-2x² - y² at the point (5,5)? (5 分) Find a line tangent to the curve f(x, y) = 0 at this point. (5 分) Note:Point (a, b) means that the projections of the point on the x and y axes have coordinates a and b, respectively, in the rectangular coordinate system in two-dimensional space.

a. Sketch the region of integration for the given iterated integral. (5 分)

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