408CF08assign1 - V ( t ) = 10( t 2 + t ). Approximate the...

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M408C Fall 2009 Assignment 1 Due Thursday, September 3 Be sure that you have read and understood sections 2.1, 2.2, and 2.3 before you complete this assignment. You must show sufficient work in order to receive full credit for a problem. Please write legibly and label the problems clearly. Circle your answers when appropriate. Multiple papers must be stapled together. Write your name and the time of your discussion section on each page. Homework is to be turned in at the beginning of the discussion section. You may use calculators for arithmetic. I strongly discourage you from using a cal- culator to do any algebraic simplification, etc., since you will not be allowed to use one on the exams. Feel free to discuss these problems with your classmates. However, each student must write up his or her own solution. 1. A right cylindrical tank is being filled with water. The volume (in liters) of water in the tank t hours after the tank begins to fill is given by
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Unformatted text preview: V ( t ) = 10( t 2 + t ). Approximate the instantaneous rate at which water is entering the tank one hour after the tank begins to ll. Explain clearly how you arrive at your approximation. (You may not use derivatives!) For problems 2 and 3, evaluate each limit or explain clearly why it does not exist. 2. lim x 2 1 x-1 2 1 x-2 3. lim x -4 2 x x + 4 + 8 x + 4 4. True or false? If true, give an explanation to explain why the statement must always be true. If false, give an example to show that the statement need not hold in all cases. (a) If lim x c ( f ( x ) + g ( x )) exists,but lim x c g ( x ) does not exist, then lim x c f ( x ) does not exist. (b) If lim x c f ( x ) exists, then lim x c 1 f ( x ) exists. 5. Determine whether the limit approaches ,- , or neither. Justify your answer. lim x -1 + 2 x 2 ( x-1) ( x + 1) 3...
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