11Breview5

11Breview5 - ucsc econ/ams 11b Review Questions 5 Indenite...

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ucsc econ/ams 11b Review Questions 5 Indefinite Integrals and Applications 1. Compute the following integrals a. Z 3 xdx 3 x 2 + 1 = b. Z ( x 2 + 2 x )( x 3 + 3 x 2 - 1) 3 dx = c. Z dx x ln x = d. Z ( x 2 + x )( x 3 + x 2 - 1) 2 dx = e. Z 3 x · e x 2 +1 x 2 + 1 dx = f. Z 1000 e - 0 . 05 t dt = g. Z 7 · 5 3 t dt = h. Z 2 + x 2 x + 1 dx = 2. A firm’s marginal cost function is dc dq = 2(5 q +100) 1 / 2 , and their fixed cost is $10000. Find the firm’s cost function. 3. A firm’s marginal revenue and marginal cost functions are dr dq = 200 - (2 q + 8) 2 / 3 and dc dq = 0 . 2 q + 65 , respectively. How will the firm’s profit change if output is increased from q = 100 to q = 200? 4. A firm’s marginal revenue function is given by
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