Question

Find the limit as x approaches zero of (the square root of (x^6+9)-3)/x^6

Answer 1

\[\lim_{x \rightarrow 0}\frac{ \sqrt{x^6+9}-3 }{ x^6 }\]

please no l'hopital's rule. I'm suposed to be able to transform it algebraically. The answer is 1/6, I just don't know how to get there

Answer 2

Try to rationalize the numerator.

Answer 3

what does that mean?

Answer 4

multiply and divide by sqrt(x^6 +9) + 3
See if it helps ?

Answer 5

Ok i get to this point:

Answer 6

\[\frac{ x^6+9-3 }{ x^6(\sqrt{x^6+9}+3) }\]

Answer 7

Is that right and then how do i get past that?

Answer 8

In the numerator, in place of -3, there should be -9 , check that.

Answer 9

got it! thanks!

Answer 10

Glad you did. ^_^