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 2 years ago
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
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.

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

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

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

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

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

Mark_CZE
 2 years ago
Best ResponseYou've already chosen the best response.0Yes. I had the same as you in your last post, but I forgot the and put there only 3 instead. Which was really silly.

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

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

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

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

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

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

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

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

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

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

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

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

Mark_CZE
 2 years ago
Best ResponseYou've already chosen the best response.0Thank 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.
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