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Unformatted text preview: Project 8 MAC 2311 1. Remember that infinity is not a number with which we can perform algebraic operations. When we write infinity as a limit, it means “a number becoming arbitrarily large”. But, we’ve seen there are some “operations” we can perform by thinking of what limits truly mean. If we divide a constant by larger and larger numbers, then the result is smaller and smaller (close to zero). If we have two very large positive numbers, then their sum or product is even larger. Thus, in the sense of limits , we can say that ∞ + ∞ = ∞ , ∞ · ∞ = ∞ , and 1 ∞ = 0 . Similary, if a function f ( x ) approaches L as x → ∞ , then it means nothing more than: the “outputs” of f become close to L when the “inputs” are made large. It does not matter how you arrive at the inputs, as long as they can be made as large as imaginable in the limit. Use these ideas to evaluate the limits below by reasoning alone , without picking up a pencil....
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