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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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- Spring '06