Question

Where did $\sqrt{x^2/x^2}$ come from in $\lim_{x \to -\infty}\frac{x+1}{\sqrt{x^2}} = \lim_{x \to -\infty}\frac{-1-1/x}{\sqrt{x^2/x^2}} = -1$?

score 126 · Answer 1 · 2016-06-03 15:54:13

Where did $\sqrt{x^2/x^2}$ come from in $\lim_{x \to -\infty}\frac{x+1}{\sqrt{x^2}} = \lim_{x \to -\infty}\frac{-1-1/x}{\sqrt{x^2/x^2}} = -1$?

score 199 · Answer 2 · 2016-06-04 17:11:30

199

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List Question

Where did $\sqrt{x^2/x^2}$ come from in $\lim_{x \to -\infty}\frac{x+1}{\sqrt{x^2}} = \lim_{x \to -\infty}\frac{-1-1/x}{\sqrt{x^2/x^2}} = -1$?

Why can't we just say that $\infty-\infty$ equals zero?

Proof of equivalent condition for $\sum_{x\in X}f(x)$ being absolutely convergent (Lemma 8.2.3 in Tao's Analysis 1)

Is this sequence going to infinity, and how do we know that?

Infinite differentiability with a removable discontinuity?

What are the limit points of $A_n=[n,\infty)$ in a metric space? Is $A_n$ closed?

Topology and Borel sets of extended real line

How $\infty=\infty$.

What's so different about limits compared to infinitesimals?

Different sizes of infinity

Inverse of a matrix with main diagonal elements approaching infinity

Random walk on a segment with infinite time

1/$\aleph$ and probability

Infinity/exponential problems.

Paradox of Infinity?

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