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There are multiple ways to interpret this question-that is, you could mean either (5-x+cosx)/x or 5-x +(cosx/x). The limit of the second option is negative infinity because as x approaches infinity, |cosx/x|≤1, so 5-x+cosx/x is very close to 5-x, and 5-infinity is basically negative infinity. For the first option, we consider that -1≤cosx≤1. This implies that, as x approaches infinity, lim of (5-x-1)/x≤lim of (5-x+cosx)/x≤lim of (5-x+1)/x. Simplifying, we get that, as x approaches infinity, lim of (4-x)/x≤lim of (5-x+cosx)/x≤(6-x)/x. Simplifying our new limits, we get -1≤lim of (5-x+cosx)/x≤1. It is now clear that the limit of (5-x+cosx)/x as x approaches infinity =negative 1.

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Q: What is the Limit as X approaches infinity 5-X plus cosXoverX?
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