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u
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b
Let m = 1 – 2. Let k = 0.9 + m. Let i be ((-2)/6)/(30/(-36)) – 0. Which is the third biggest value? (a) k (b) 0 (c) i
a
Let p = -0.05 + -0.04. Let t = 0.11 + p. Let f = 0.14 + t. Which is the smallest value? (a) f (b) -0.2 (c) 2
b
Let t = 0.36 – 0.06. Let z = 13.8 + -14. Let o = z + 0.1. What is the third smallest value in -4, t, o?
t
Let x = 0 – -5. Let v = 0.3 – 0.3. Which is the second smallest value? (a) x (b) v (c) 1
c
Let o = -1.2 + 2.2. Which is the second smallest value? (a) o (b) -2/11 (c) -0.2
b
Let i = 0.6 + -2.6. Let g = -7/3 + 2. What is the smallest value in -4/9, i, g?
i
Let k = -3 – -2.6. Let x = 4.4 + 0.6. Let v = 0.1 + -0.6. Which is the third smallest value? (a) k (b) v (c) x
c
Let p(s) = s**2 + 5*s + 5. Let o be p(-4). Let v be o + ((-15)/28)/1. Which is the second smallest value? (a) -4 (b) v (c) -0.1
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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
$$\sqrt{|\Delta(z)|} = \sqrt{\Delta(z)} = \sqrt{z^2 + z + 1} \underset{|z|\to+\infty}{\longrightarrow} 1.$$

HERUS

Launched in Spring 2012 as a pure romance and adventure to pursue solo travel, herus is a contemporary bicycle-touring brand with a political twist. Dedicated to the pursuit of great outdoor experiences, sheus provides women riders with a brand of feminine design, superior craftsmanship, and a highly authentic spirit of adventure.

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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