Handout (Respective Rates of Change) (Schwartz; Math 157) Work the problems on your own paper just like a normal homework assignment. 1. Let ? = √?. (a) Find ?? ?? and simplify your answer. (b) Find ?? ?? and simplify your answer. (c) How are ?? ?? and ?? ?? related? (d) Find ?? ?? and ?? ?? when ? = 9. 2. Boyle’s law states that the pressure, ?, exerted by an ideal gas is inversely proportional to the volume, ?, it occupies, provided the temperature remains constant. This means that ?? = ? where k is a constant. Find ?? ?? . 3. The volume for a cylinder of radius ? and height ℎ is given by ? = ?? 2ℎ. (a) Find the rate of change of ? with respect to ℎ if we want the volume to remain constant. (b) Find the rate of change of ℎ with respect to ? if we want the volume to remain constant. (c) Find the rate of change of ? with repect to ? if we want the height to remain constant. (d) Find the rate of change of ? with repect to ℎ if we want the radius to remain constant. 4. Suppose that we can sell ? Thingys if we set the price of a Thingy at $?. Market research shows that the relationship between price and demand is given by ? = −0.2? + 70. (a) Find and explain the meaning of each of the following in the context of this application. Be specific with respect to values and units. i. ?? ?? ii. ?? ?? (b) Find the revenue, ?, as a function of p. (c) Find the revenue, ?, as a function of x. (d) Suppose that the cost of producing ? Thingys is given by ?(?) = 2,000 + 6?. i. Find the profit, ?, as a function of p. ii. Find ?? ?? . iii. Find the profit, ?, as a function of x. iv. Find ?? ?? . (e) Find and explain the meaning of each of the following in the context of this application. Be specific with respect to values and units. i. ?? ?? when the price of a Thingy is $50. ii. ?? ?? when the price of a Thingy is $50. iii. ?? ?? when the price of a Thingy is $50. iv. ?? ?? when the price of a Thingy is $50.

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Status NEW Posted 15 Aug 2017 05:08 PM My Price 10.00

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