How Do You Solve a Limit Involving Infinity in Polynomial Functions?

[mohamedibr752]

Hi, I'm in Engineering Foundation.
I'm stuck in one limit question.

Find the limit :_
**********________
Lim (3x + V 9x^2 - x )
x-> -infinity

by substitution it gives ( inf - inf )
I tried to solve it and get -inf

Can anyone help me please ?

 

[tiny-tim]

Welcome to PF!

Hi mohamedibr752! Welcome to PF!

(have a square-root: √ and an infinity: ∞ )

Hi, I'm in Engineering Foundation.
I'm stuck in one limit question.

Find the limit :_
**********________
Lim (3x + V 9x^2 - x )
x-> -infinity

by substitution it gives ( inf - inf )
I tried to solve it and get -inf

Can anyone help me please ?

(no need to shout! )

Hint: it's the same as lim_x->-∞ 3x + 3|x|√(1 - 1/9x))

 

[mohamedibr752]

Thank you for your help .. I get it now ..
but why did you write it 3x(1 + ...
I think it is 3x(1 - ...
because the x is approaching -∞ so as to remove absolute 3x we have to put - to make sure that the 3x is positive ??

The answer I get is -∞.

Thank you

 

[tiny-tim]

Hi mohamedibr752!

but why did you write it 3x(1 + ...
I think it is 3x(1 - ...

I goofed!

I did correct it before you answered, but I think you missed the change.

The answer I get is -∞.

No, try again … expand the square-root and do a bit of cancelling.

 

[Mentallic]

The answer I get is -∞.

Wait, what? No the answer isn't -\infty.

Look again at 3x+3|x|\sqrt{1-\frac{1}{9x}} as the limit approaches -\infty. It is definitely not what you stated.

 

[evagelos]

Hi, I'm in Engineering Foundation.
I'm stuck in one limit question.

Find the limit :_
**********________
Lim (3x + V 9x^2 - x )
x-> -infinity

by substitution it gives ( inf - inf )
I tried to solve it and get -inf

Can anyone help me please ?

Multiply by \frac{3x -\sqrt{9x^2-x}}{3x-\sqrt{9x^2-x}} ... and then divide by x,


then take the limit