Fa2010-Prelim_2

# A 8 points supposing that we increase the temperature

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(a) ( 8 points ) Supposing that we increase the temperature at a rate of 1000 degrees per sec- ond, how quickly is the power output increasing when the temperature is 4500 degrees? Do not simplify your answer. CONTINUE TO NEXT PAGE

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Math 1110 Fall 2010 Prelim 2 October 28, 2010 7 Problem 4: (cont.) (b) ( 4 points ) Suppose that in some alternate universe, physicists measured that P = tan - 1 (1 + T ) . If our alternate universe selves increase the temperature at a rate of 1000 degrees per second, find a formula for dP dt . (c) ( 3 points ) Using your solution from part (b), compute lim t →∞ dP dt . CONTINUE TO NEXT PAGE
Math 1110 Fall 2010 Prelim 2 October 28, 2010 8 Problem 5: ( 20 points ) Determine whether the following statements are (always) true or (sometimes) false, and clearly mark each TRUE or FALSE accordingly. If you think a statement is true, show and explain why (in complete sentences). If you think a statement is false, provide an example where it fails to be true, and explain your example (in complete sentences). (a) ( 5 points ) If f ( x ) is a one-to-one function with f 0 ( x ) > 0 for all x , then the derivative of f - 1 ( x ) is greater than zero where it is defined.

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• Fall '06
• MARTIN,C.
• Continuous function

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