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I'm a bit puzzled with a limit, as is my teacher. We came across a question that could be both factored or rationalized, but when factored, the answer is different. Perhaps someone has an explanation?

Here it is.

lim ((√x^2+4x)-x)

x->∞

I'm not going to rationalize it, because I know that is right. I'm going to show you how I'm factoring it, and perhaps someone can explain why it is not working. Thanks

lim ((√x^2+4x)-x)

x->∞

lim (x(√1+4/x)-x)

x->∞

lim x((√1+0)-1)

x->∞

lim x(0)

x->∞

lim = 0

x->∞

....

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# Homework Help: Fnd the limit of sqrt(x^2 + 4x) - x as x goes to infinity

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