Lesson05_-_Continuity_ws

Lesson05_-_Continuity_ws - 2. For what value(s) of c is f (...

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Worksheet for Section 1.5 Continuity V63.0121, Calculus I Spring 2010 1. Which of the following functions are continuous? (i) The temperature of a pie as it is taken from the freezer to the oven to the table. (ii) The temperature at a specific moment along the equator as a function of longitude. (iii) The time to wait for a subway train, as a function of the time arrived at the station. (iv) The cost of parking in a garage as a function of the time parked. (v) The production of a firm as a function of capital invested. (vi) The amount of taxes owed as a function of taxable income.
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Unformatted text preview: 2. For what value(s) of c is f ( x ) = ( cx 2 + 2 x if x < 2 x 3-cx if x 2 continuous? 1 3. Use the Intermediate Value Theorem to show that x 4 + x = 3 has a root in the interval (1 , 2). 4. A monk leaves the monastery at 7:00 AM and takes his usual path to the top of the mountain, arriving at 7:00 PM. The following morning, he starts at 7:00 AM at the top and takes the same path back to the monastery, arriving at 7:00 PM. Is there a point on the path that the monk will cross at exactly the same time of day on both days? Why or why not. 2...
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This note was uploaded on 07/19/2010 for the course MATH V63.-0121- taught by Professor Staff during the Spring '08 term at NYU.

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Lesson05_-_Continuity_ws - 2. For what value(s) of c is f (...

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