Finding Limit x -> Infinity of y = 2x^2/(a+2x)

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To find the limit as x approaches infinity for the function y = 2x^2/(a + 2x), the expression can be simplified to y = 2x^2/(2x(1 + a/(2x))). As x approaches infinity, the term a/(2x) approaches zero, leading to y simplifying to y = x. Therefore, the limit of y as x approaches infinity is infinity, indicating that the function diverges. The discussion highlights confusion about the evaluation process and the simplification steps involved. Understanding the behavior of the function at infinity is crucial for determining its limit.
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I need to find the limit x -> infinity of the following:

y = x ( (2x/a) / (1 + (2x/a)) )

Simplifying..

y = x ( (2x/a) / ((a + 2x)/a) )

y = x ( 2x / (a + 2x) )

y = 2x^2 / (a + 2x)

Is this even right in the first place? because I have no idea how to evaluate the lim x -> infinity.
 
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