# Re: Using algebra when solving limits

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Posted by mfrizza on October 15, 2002 at 20:03:16:

In Reply to: Re: Using algebra when solving limits posted by Joel on October 15, 2002 at 17:39:37:

Thanks for the explanation. I know this is an easy concept, but I'm still struggling to understand why the x becomes x^2 when you put it inside the sqrt. Why doesn't it just stay as x?

: : Help! I'm missing the point here...

: : half way through this limits -> inf. problem and I'm stuck on a basic algebra issue...

: : lim x-> inf.

: : x / sqrt(9x^2+ x) + 3x

: : next step...divide both sides by largest x in denominator...okay, let's use x

: : x/x / sqrt(9x^2 + x)/x + 3x/x

: : now we have 1 / sqrt(9x^2 + x)/x + 3...

: : I don't understand the mechanics of sqrt(9x^2 + x)/x ....how does that work!

: Assuming that 3x term is in the denominator, you should show it as x / (sqrt(9x^2+ x) + 3x).

: The next step is to put that x inside the sqrt

: = 1 / (sqrt((9x^2 + x)/x^2) + 3)
: = 1 / (sqrt((9 + 1/x) + 3)
: as x->infinity (1/x)->0 so you're left with
: 1 / (sqrt(9) + 3) = 1/6

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