11Breview8 - econ 11b ucsc ams 11b Review Questions 8 Table...

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econ 11 b ucsc ams 11 b Review Questions 8 Table of integrals and differential equations 1. Compute the following integrals a. Z 5 x 7 - 2 x dx = b. Z 7 t 2 + 3 t - 1 2 + 5 t dt = c. Z 500 t 2 e - 0 . 04 t dt = d. Z 3 e 2 x 4 + e x dx = e. Z 300 1 + 0 . 25 e - 0 . 1 t dt = f. Z 4(ln x ) 2 3 x 2 + 7 ln x dx = 2. Let y = f ( x ) satisfy (i) dy dx = 3 xy 2 and (ii) y (1) = 2. Find the function f ( x ). 3. The income-elasticity of demand for a firm’s product is proportional to the square root of income. Find the demand as a function of income, given that q (100) = 50 and q (400) = 90. 4. The population of a tropical island grows at a rate that is proportional to the third root ( 3 ) of its size. In 1950, the islands population was 1728 and in 1980, the islands population was 2744. What will the Islands population be in 2020?
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