# Thread: limit to negative infinity

1. ## limit to negative infinity

Use a table of values of f(x) to estimate the value of the limit to four decimal places.

idk if I am just not knowing how to do this, but if someone could walk me through this I would be more than greatful!

2. Originally Posted by ryan18
Use a table of values of f(x) to estimate the value of the limit to four decimal places.

idk if I am just not knowing how to do this, but if someone could walk me through this I would be more than greatful!
what about using the "trick" that i showed you in the other post?

3. Originally Posted by felper
what about using the "trick" that i showed you in the other post?
What do you mean? Multiplying it by the same thing just a + instead of a -? Sorry I am horrible with LaTeX I tried, but it didnt turn out right.

4. Yeah. See that link http://www.wolframalpha.com/input/?i=limit+x+to+-infinity+(sqrt(3x^2%2B4x%2B5)-sqrt(3x^2%2B3x%2B7)) and try the "technique" that i told you.

5. $\displaystyle \lim_{x\rightarrow-\infty} \sqrt{3x^2+4x+5}-\sqrt{3x^2+3x+7}$

$\displaystyle \lim_{x\rightarrow-\infty} \sqrt{3x^2+4x+5}-\sqrt{3x^2+3x+7}\frac{(\sqrt{3x^2+4x+5}+\sqrt{3x^2 +3x+7})}{(\sqrt{3x^2+4x+5}-\sqrt{3x^2+3x+7})}$

$\displaystyle \lim_{x\rightarrow-\infty}\frac{3x^2+4x+5-(3x^2+3x+7)}{\sqrt{3x^2+4x+5}+\sqrt{3x^2+3x+7}}$

$\displaystyle \lim_{x\rightarrow-\infty}\frac{x-2}{\sqrt{3x^2+4x+5}+\sqrt{3x^2+3x+7}}$

$\displaystyle \lim_{x\rightarrow-\infty}\frac{-(x-2)/|x|}{(\sqrt{3x^2+4x+5}+\sqrt{3x^2+3x+7})/|x|}$

$\displaystyle \lim_{x\rightarrow-\infty}\frac{-(1-\frac{2}{x})}{\sqrt{3+\frac{4}{x}+\frac{5}{x^2}}+\ sqrt{3+\frac{3}{x}+\frac{7}{x^2}}}$

$\displaystyle \lim_{x\rightarrow-\infty}\frac{-(1-0)}{\sqrt{3+0+0}+\sqrt{3+0+0}}$

$\displaystyle \lim_{x\rightarrow-\infty}\frac{-1}{\sqrt{3}+\sqrt{3}}=\frac{-1}{2\sqrt{3}}$

Holy mother I can't believe I typed that all out.

6. There was a solution already posted similar to this question here:

7. Wouldn't it be better to do what the problem told you to do?

The problem said "Use a table of values of f(x) to estimate the limit to four decimal places".

When x= -1000, that expression is -0.2894.
When x= -1000000 that expression is -0.2887.

etc.