Having problems solving a problem with a single limit?

[JP7PlaysMC]

Hello fellow readers and posters of this forum.

Recently I've been trying to solve a limit and I'm a loss for how it can be done. No matter what I do it always ends up in one type of indetermination (either -infinit+infinit or infinit*0).
The problem is as follows: Lim 3x-sqrt{9x^2+5}

I've tried everything from taking the X outside of the square root and even doubling the root (as such Lim 3x-(sqrt{9x^2+5}*sqrt{9x^2-5})/sqrt{9x^2-5}, but to no avail.

Can you help me out or at least point out some things for me to try? I'm in 11th grade, so I'm not that knowledgeable in Calculus.

 

[Deleted member 4993]

Hello fellow readers and posters of this forum.

Recently I've been trying to solve a limit and I'm a loss for how it can be done. No matter what I do it always ends up in one type of indetermination (either -infinit+infinit or infinit*0).
The problem is as follows: Lim 3x-sqrt{9x^2+5}

I've tried everything from taking the X outside of the square root and even doubling the root (as such Lim 3x-(sqrt{9x^2+5}*sqrt{9x^2-5})/sqrt{9x^2-5}, but to no avail.

Can you help me out or at least point out some things for me to try? I'm in 11th grade, so I'm not that knowledgeable in Calculus.

View attachment 7896

Limit to what?

\(\displaystyle \displaystyle{x \ \to 0}\)

or

\(\displaystyle \displaystyle{x \ \to \infty}\)

or

\(\displaystyle \displaystyle{x \ \to (something else)}\)

 

[JP7PlaysMC]

Limit to what?

\(\displaystyle \displaystyle{x \ \to 0}\)

or

\(\displaystyle \displaystyle{x \ \to \infty}\)

or

\(\displaystyle \displaystyle{x \ \to (something else)}\)

[FONT=MathJax_Math-italic]x[/FONT][FONT=MathJax_Main] [/FONT][FONT=MathJax_Main]→[/FONT][FONT=MathJax_Main]∞, I'm sorry, that's the only limits we're working with.[/FONT]

 

[stapel]

...No matter what I do it always ends up in one type of indetermination (either -infinit+infinit or infinit*0).
The problem is as follows: Lim [x->infty] 3x-sqrt{9x^2+5}

The standard step for this sort of expression is to multiply by the conjugate.

. . . . .\(\displaystyle \left(\dfrac{3x\, -\, \sqrt{\strut 9x^2\, +\, 5\,}}{1}\right)\left(\dfrac{3x\, +\, \sqrt{\strut 9x^2\, +\, 5\,}}{3x\, +\, \sqrt{\strut 9x^2\, +\, 5\,}}\right)\)

. . . . .\(\displaystyle \dfrac{9x^2\, -\, (9x^2\, +\, 5)}{3x\, +\, \sqrt{\strut 9x^2\, +\, 5\,}}\)

...and so forth. Where does this lead?

 

[JP7PlaysMC]

Thanks a lot! I was beggining to suspect I had to multiply by the whole thing. Kind of a begginer mistake I guess. I was able to finish the exercise!