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. Q:
Limit of $\sqrt{|\Delta(z)|}$ as $|z| \rightarrow \infty$.
It is given that $$\lim_{z \rightarrow \infty} \sqrt{|\Delta(z)|} = 1.$$ I have tried to use the formula for $\Delta(z)$ given by:
$$\Delta(z) = z – (z^2+1)/(z+1).$$
However, I still don’t know how to deal with the $\sqrt{|\Delta(z)|}$ term. I am looking to extend my solution to general case where $|\Delta(z)|$ could be a quadratic polynomial and then try to consider each case to prove that the limit is 1.
A:
As $\Delta(z) = z^2 + z + 1$, one has
$$\sqrt{|\Delta(z)|} = \sqrt{\Delta(z)} = \sqrt{z^2 + z + 1} \underset{|z|\to+\infty}{\longrightarrow} 1.$$
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Chris Blythe
Chris Blythe is a Canadian bicycle builder who loves adventure. He makes handmade handmade bicycles and is the founder of HERUS, a brand dedicated to the pursuit of great outdoor experiences. Chris is one of the faces of the HERUS brand and has been featured in a variety of media and events including Globe & Mail, Outside, TIME, and NBC TV. He is actively working to promote cycling as a great form of transportation.
After leaving a corporate life to pursue a career as a bicycle builder in Richmond, England, Chris launched HERUS in 2012. Chris has been riding and building bikes since he was a teenager
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