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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.
 one year ago
 one year 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.
 one year ago
 one year ago

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

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

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

Mark_CZEBest 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 :)
 one year ago

myininayaBest ResponseYou've already chosen the best response.1
\[\lim_{x \rightarrow \infty}\frac{\sqrt{\frac{x^2+8}{x^2}}\frac{3}{x}}{\frac{1}{x}1}\]
 one year ago

myininayaBest ResponseYou've already chosen the best response.1
the answer shouldn't be 1 ...
 one year ago

Mark_CZEBest 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.
 one year ago

Mark_CZEBest ResponseYou've already chosen the best response.0
You forgot something. The x before those expressions.
 one year ago

Mark_CZEBest ResponseYou've already chosen the best response.0
Now I am getting a 1, as you are implying. Thats weird. I need to recheck.
 one year ago

myininayaBest ResponseYou've already chosen the best response.1
What do you mean the x before the expressions?
 one year ago

myininayaBest ResponseYou've already chosen the best response.1
right 1 is what i got
 one year ago

Mark_CZEBest 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...
 one year ago

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

Mark_CZEBest ResponseYou've already chosen the best response.0
Yes. I typed it right the first time.
 one year ago

myininayaBest 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.
 one year ago

myininayaBest ResponseYou've already chosen the best response.1
\[x=x \text{ if } x<0\]
 one year ago

Mark_CZEBest ResponseYou've already chosen the best response.0
But I still get a 1. I checked with Wolfram it gets +1.
 one year ago

Mark_CZEBest ResponseYou've already chosen the best response.0
Absolute value, Im following. Got the same.
 one year ago

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

myininayaBest ResponseYou've already chosen the best response.1
Yep the limit is 1 if x>inf
 one year ago

Mark_CZEBest 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.
 one year ago
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