Solving the limit of a function with no calculator

[APcalchelp]

The Lim_x-->infinity of the function Square rt(5x^4+2x) / (x^2)

Note* The square root is only in the numerator for the expression (5x^4+2x)



I have tried multiplying by the complex conjugate but I am not sure if this is the correct way to do it.

I did sqrt(5x^4-2x) over itself and got sqrt 25x^8-4x / x^2

I had that as my answer, but my teacher told me this was incorrect. If anyone could help and explain that would be great! Thanks a lot!

 

[Mark44]

The Lim_x-->infinity of the function Square rt(5x^4+2x) / (x^2)

Note* The square root is only in the numerator for the expression (5x^4+2x)



I have tried multiplying by the complex conjugate but I am not sure if this is the correct way to do it.

I did sqrt(5x^4-2x) over itself and got sqrt 25x^8-4x / x^2

I had that as my answer, but my teacher told me this was incorrect. If anyone could help and explain that would be great! Thanks a lot!

Factor x⁴ out of both terms inside the radical, and bring this out as x². You should be able to evaluate the limit then.

 

[APcalchelp]

Factor x⁴ out of both terms inside the radical, and bring this out as x². You should be able to evaluate the limit then.

I'm not clear on what you mean by that. I understand factoring out the x^4 from the 5x^4 but not the 2x.

 

[BrownianMan]

I'm not clear on what you mean by that. I understand factoring out the x^4 from the 5x^4 but not the 2x.

If you factor out x^4 from 2x, you are left with 2/x^3.