Posted by Joel on October 15, 2002 at 17:39:37:
In Reply to: Using algebra when solving limits posted by mfrizza on October 15, 2002 at 17:08:09:
: 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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