Question

Abit more complicated horizontal asymptote question, how do i approach this?

Answer 1

do i rationalize it? its hard to take out the x^3 term because of the squareroot..

Answer 2

hm i actually squared both num and denom, and i got 1/80 is that correct?

Answer 3

no dont rationalize it, rewrite the insides of the squareroot as sqrt((x^6)(64+1/x^6))-->. (x^3)sqrt(64+1/x^6))With this u will be able to take everything into x^3 paranthesis. careful though since the power is odd it can either be positive or negative. The final answers are: 1/12 and -1/4

Answer 4

\[\sqrt{(x^6)(\frac{ 64+1 }{ x^6 })}\] u eman like this?

Answer 5

*mean

Answer 6

yes correct, when taking the x^6 out it becomes x^3. but you have a +- sign infront of it because x^6 can be the square of both -x^3 and +x^3

Answer 7

oh, so there will be 2 answers?

Answer 8

wait its not correct see its 64 + 1/x^6. 64 is on its own

Answer 9

yes there will be two answers

Answer 10

yeah its odd, idk how u come up with this, i dont follow where you are coming from, the purpose of this is to get rid of the squareroot or?

Answer 11

point is taking bot numerator and denomerator in common multiple(x^3) so you divide both by that number in the next step and get rid of it

Answer 12

\[\frac{ x^3+8 }{ 4x^3+x^3\sqrt{64+\frac{ 1 }{ x^6 }} }\] like this?