Computing Limits at Infinity Part V

[Hckyplayer8]

Compute the lim as x --> neg infinity [sqrt(x²+5x) - sqrt(x²+x)]

This limit does not exists, correct?

 

[pka]

Compute the lim as x --> neg infinity [sqrt(x²+5x) - sqrt(x²+x)]
This limit does not exists, correct?

NO! LOOK HERE
Note that \(\displaystyle \sqrt{x^2+5x}-\sqrt{x^2+x}=\frac{4x}{\sqrt{x^2+5x}+\sqrt{x^2+x}}\)

 

[Dr.Peterson]

Compute the lim as x --> neg infinity [sqrt(x²+5x) - sqrt(x²+x)]

This limit does not exists, correct?

The limit has the form [MATH]\infty - \infty[/MATH], which is indeterminate. So you have to rewrite it. This is what pka has done; if you have learned about "rationalizing the numerator", apply that (using the conjugate) thinking of your expression as a fraction with 1 in the denominator.

 

[Hckyplayer8]

Ah. I didn't see indeterminate form. I'm tracking with regard to multiplying by the conjugate and understand how pka got to that point in the problem.