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Mark_CZE
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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.
 2 years ago
 2 years ago
Mark_CZE Group Title
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.
 2 years ago
 2 years ago

This Question is Closed

Mark_CZE Group TitleBest ResponseYou've already chosen the best response.0
\[\lim_{x \rightarrow \infty} \frac{ \sqrt{x ^2 + 8} 3 }{ 1 x }\]
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
Multiply top and bottom by \[1/\sqrt{x^2}\]
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
Now since x> inf and not inf then x=x not x So we have \[\lim_{x \rightarrow \infty}\frac{\sqrt{x^2+8}3}{1x} \frac{\frac{1}{\sqrt{x^2}}}{\frac{1}{x}}\]
 2 years ago

Mark_CZE Group TitleBest ResponseYou've already chosen the best response.0
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 :)
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
\[\lim_{x \rightarrow \infty}\frac{\sqrt{\frac{x^2+8}{x^2}}\frac{3}{x}}{\frac{1}{x}1}\]
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
the answer shouldn't be 1 ...
 2 years ago

Mark_CZE Group TitleBest ResponseYou've already chosen the best response.0
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.
 2 years ago

Mark_CZE Group TitleBest ResponseYou've already chosen the best response.0
You forgot something. The x before those expressions.
 2 years ago

Mark_CZE Group TitleBest ResponseYou've already chosen the best response.0
Now I am getting a 1, as you are implying. Thats weird. I need to recheck.
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
What do you mean the x before the expressions?
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
right 1 is what i got
 2 years ago

Mark_CZE Group TitleBest ResponseYou've already chosen the best response.0
You have limit goes to infinity. It should go to infinity. Im now checking whether it has some impact on the solution...
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
So the question was suppose to be \[\lim_{x \rightarrow  \infty}\frac{\sqrt{x^2+8}3}{1x}\]
 2 years ago

Mark_CZE Group TitleBest ResponseYou've already chosen the best response.0
Yes. I typed it right the first time.
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
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.
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
\[x=x \text{ if } x<0\]
 2 years ago

Mark_CZE Group TitleBest ResponseYou've already chosen the best response.0
But I still get a 1. I checked with Wolfram it gets +1.
 2 years ago

Mark_CZE Group TitleBest ResponseYou've already chosen the best response.0
Absolute value, Im following. Got the same.
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
\[\lim_{x \rightarrow  \infty}\frac{\sqrt{x^2+8}3}{1x} \cdot \frac{\frac{1}{\sqrt{x^2}}}{\frac{1}{\sqrt{x^2}}}\] \[\lim_{x \rightarrow \infty}\frac{\sqrt{\frac{x^2+8}{x^2}}\frac{3}{x}}{\frac{1}{x}\frac{x}{x}}\]
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
Yep the limit is 1 if x>inf
 2 years ago

Mark_CZE Group TitleBest ResponseYou've already chosen the best response.0
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.
 2 years ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
lol. Thanks.
 2 years ago
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