Posted by rudy on Thursday, January 24, 2008 at 4:10am.
The answer depends upon whether the x^2 is in the denominator, and whether you mean sqrt 4 + x^2 or sqrt (4 + x^2). You need to use parentheses to clarify the meaning.
If you mean -x/[sqrt (4 + x^2)]
Then limit as x-> infinity = -1, because the 4 becomes negligible compared to x^2
If x^2 is a separate term, then the limit is infinity
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