anonymous
  • anonymous
One limit keeps slipping through my fingers. lim_{x rightarrow -infty} \frac{ sqrt{x ^2 + 8} -3 }{ 1- x } . The answer =1, but I keep getting =2. I will be posting my steps, please tell me when I'm wrong.
Calculus1
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
\[\lim_{x \rightarrow -\infty} \frac{ \sqrt{x ^2 + 8} -3 }{ 1- x }\]
myininaya
  • myininaya
Multiply top and bottom by \[1/\sqrt{x^2}\]
myininaya
  • myininaya
Now since x-> inf and not -inf then |x|=x not -x So we have \[\lim_{x \rightarrow \infty}\frac{\sqrt{x^2+8}-3}{1-x} \frac{\frac{1}{\sqrt{x^2}}}{\frac{1}{x}}\]

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anonymous
  • anonymous
Oh, Ive got it... Im sorry everyone. Now I see, I was making one very silly mistake. I didnt have the top part - I did not multiply the -3, which got me the wrong direction.. Thanks for the answer @myiniaya . My bad :-)
myininaya
  • myininaya
\[\lim_{x \rightarrow \infty}\frac{\sqrt{\frac{x^2+8}{x^2}}-\frac{3}{x}}{\frac{1}{x}-1}\]
myininaya
  • myininaya
the answer shouldn't be 1 ...
anonymous
  • anonymous
Yes. I had the same as you in your last post, but I forgot the and put there only -3 instead. Which was really silly.
anonymous
  • anonymous
You forgot something. The x before those expressions.
anonymous
  • anonymous
Now I am getting a -1, as you are implying. Thats weird. I need to recheck.
myininaya
  • myininaya
What do you mean the x before the expressions?
myininaya
  • myininaya
right -1 is what i got
anonymous
  • anonymous
You have limit goes to infinity. It should go to -infinity. Im now checking whether it has some impact on the solution...
myininaya
  • myininaya
So the question was suppose to be \[\lim_{x \rightarrow - \infty}\frac{\sqrt{x^2+8}-3}{1-x}\]
anonymous
  • anonymous
Yes. I typed it right the first time.
myininaya
  • myininaya
I completely didn't see the negative infinity when I read it the first time as you can see in that one comment I made above.
myininaya
  • myininaya
\[|x|=-x \text{ if } x<0\]
anonymous
  • anonymous
But I still get a -1. I checked with Wolfram it gets +1.
anonymous
  • anonymous
Absolute value, Im following. Got the same.
myininaya
  • myininaya
\[\lim_{x \rightarrow - \infty}\frac{\sqrt{x^2+8}-3}{1-x} \cdot \frac{\frac{1}{\sqrt{x^2}}}{\frac{1}{\sqrt{x^2}}}\] \[\lim_{x \rightarrow -\infty}\frac{\sqrt{\frac{x^2+8}{x^2}}-\frac{3}{-x}}{\frac{1}{-x}-\frac{x}{-x}}\]
myininaya
  • myininaya
Yep the limit is 1 if x->-inf
anonymous
  • anonymous
Thank you very much. I completely lost the one '-' sign. You cleared everything out. And btw. I dont understand how come you are so fast with putting such expressions through the keyboard on the screen. Youve earned a medal from me. Thank you.
myininaya
  • myininaya
lol. Thanks.

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