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

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SUMMARY

The limit as x approaches infinity for the function y = 2x^2/(a + 2x) can be evaluated by simplifying the expression. The correct simplification leads to y = 2x^2/(a + 2x), which can be further analyzed by dividing both the numerator and denominator by x. This results in the limit being determined as 2, since the dominant term in the numerator and denominator is 2x as x approaches infinity. Thus, the limit is conclusively 2.

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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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If you were to divide the numerator by the denominator what would you get?
 

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