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\[\lim_{x \rightarrow -\infty} \frac{ \sqrt{x ^2 + 8} -3 }{ 1- x }\]

Multiply top and bottom by \[1/\sqrt{x^2}\]

\[\lim_{x \rightarrow \infty}\frac{\sqrt{\frac{x^2+8}{x^2}}-\frac{3}{x}}{\frac{1}{x}-1}\]

the answer shouldn't be 1
...

You forgot something. The x before those expressions.

Now I am getting a -1, as you are implying. Thats weird. I need to recheck.

What do you mean the x before the expressions?

right -1 is what i got

So the question was suppose to be
\[\lim_{x \rightarrow - \infty}\frac{\sqrt{x^2+8}-3}{1-x}\]

Yes. I typed it right the first time.

\[|x|=-x \text{ if } x<0\]

But I still get a -1. I checked with Wolfram it gets +1.

Absolute value, Im following. Got the same.

Yep the limit is 1 if x->-inf

lol. Thanks.