handout_10_09

# handout_10_09 - of s miles per hour for one hour 1 What are...

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Math 1a: Product/quotient rules and applications October 9, 2009 1. Determine the following derivatives. 1. d dt ( te t ). 2. d ds ( s 3 2 s ). 3. d dp ± p 2 p 2 + 1 ² . 2. Diﬀerentiate the following functions of x in two diﬀerent ways. Check that your answers agree. Which way was easier? 1. a x b x 2. ( x 3 + 2)(4 x 2 - 1) 3. 4 x + 3 x 2 x 3. On what interval is the function f ( x ) = x 3 e x increasing? 1

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4. Two reactions take place in a beaker, represented by the following chemical equations: X + 3 A -→ Y, M -→ 2 A + N. The compound N is produced at the rate of 3 t 2 + 2 moles/liter per second, where t is the number of seconds after the reactions begin. If the concentration of compound A at time t is t 3 + 2 t + 4 moles/liter, at what rate is Y being produced at time t ? 5. Suppose that C ( s ) gives the number of calories that an average adult burns by walking at a steady speed
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Unformatted text preview: of s miles per hour for one hour. 1. What are the units of dC ds ? 2. Do you expect dC ds to be positive? Why or why not? 3. Interpret the statement C (3) = 25. 6. The cost of producing x items of a certain commodity, in dollars, is C ( x ) = 100 + 3 x-. 001 x 2 + 0 . 000001 x 3 . 1. How might we interpret the 100 and the 3? (What are their units?) 2. In fact C ( x ) is always positive. Why would you expect this? 3. A company produces 100 items and sells them at \$2 . 90 each. Assuming it could sell more at the same price, should it produce more? 2...
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handout_10_09 - of s miles per hour for one hour 1 What are...

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