<div>
Your solution from step 4 looks too complex, where would you take it?<br />
<br />
But you gave me an idea.<br />
lim(ln(x+sqrt(x^2+1)), x-&gt;-infinity) = lim(ln(x+abs(x)*sqrt(1+1/x<wbr />^2)),x-&gt;-i<wbr />nfinity) =<br />
lim(x - x*sqrt(1+1/x^2), x -&gt; - infinity) = lim(x*(1-sqrt(1+1/x^2)), x -&gt; - infinity)) =<br />
lim(ln(x) + ln(1-sqrt(1+1/x^2)), x -&gt; - infinity) = 0 - infinity = -infinity<br />

</div>


Your solution from step 4 looks too complex, where would you take it?

But you gave me an idea.
lim(ln(x+sqrt(x^2+1)), x->-infinity) = lim(ln(x+abs(x)*sqrt(1+1/x^2)),x->-infinity) =
lim(x - x*sqrt(1+1/x^2), x -> - infinity) = lim(x*(1-sqrt(1+1/x^2)), x -> - infinity)) =
lim(ln(x) + ln(1-sqrt(1+1/x^2)), x -> - infinity) = 0 - infinity = -infinity


<div>
<div class="content wysiwyg-content">
Hello,<br />
<br />
how would you solve this limit?<br />
<br />
lim(ln(x+sqrt(x^2+1)), x -&gt; - infinity)<br />
<br />
I have done these steps lim(ln(1/(1/x) + 1/(1/sqrt(x^2+1)), x= -infinity) = lim(ln((1/sqrt(x^2+1)+1/x)<wbr />/(1/(x*sqr<wbr />t(x^2+1)))<wbr />), x = -infinity)<br />
now I would use l'Hopital rule. But this don't look nice<br />
<br />
Is there some easier method?<br />
<br />
thanks
</div>
</div>


Hello,

how would you solve this limit?

lim(ln(x+sqrt(x^2+1)), x -> - infinity)

I have done these steps lim(ln(1/(1/x) + 1/(1/sqrt(x^2+1)), x= -infinity) = lim(ln((1/sqrt(x^2+1)+1/x)/(1/(x*sqrt(x^2+1)))), x = -infinity)
now I would use l'Hopital rule. But this don't look nice

Is there some easier method?

thanks

lim(ln(x+sqrt(x^2+1)), x -&gt; - infinity)

The Math / Science topic primarily includes discussions of mathematics, physics, statistics and economic analysis, but also biology, chemistry and other sciences.

lim(ln(x+sqrt(x^2+1)), x -&gt; - infinity)

lim(ln(x+sqrt(x^2+1)), x -> - infinity)