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研究所、轉學考(插大)-微積分
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103年 - 103 國立臺灣師範大學_學士班轉學生招生考試試題_機電工程學系二年級：微積分#120325
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3. Differentiate x² log₁₀(2x²+3). (5 分)
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c. How many databases still needed to be transferred in 2009? (5 points)
#512563
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)
#512564
1. Find the radius of convergence and interval of convergence for the given power series. (5 分)
#512565
2. Consider the function . Find f'(x). (5 分)
#512566
4. Approximate cosx by a fourth-degree polynomial for values of x close to 0. (5 分)
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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)
#512569
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.
#512570
a. Sketch the region of integration for the given iterated integral. (5 分)
#512571
b. Change or reverse the order of integration. In other words, rewrite the integral in the form of . (5 分)
#512572
8. The function f is defined by . Evaluate f(1). (10 分)
#512573
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