a-positive-number-epsilon-and-the-limit-l-of-a-function-f-at-infty-are-given-find-a-negative-numb-16

Question

A positive number $\epsilon$ and the limit $L$ of a function $f$ at $-\infty$ are given. Find a negative number $N$ such that $|f(x)-L|<\epsilon$ if $x<N$.
$$\lim _{x \rightarrow-\infty} \frac{1}{x^{2}}=0 ; \epsilon=0.01$$

R M · Accepted Answer

a problem. Number 46. Assume X is negative. Ah, went over Excess words upset you. It&#x27;s one of that. All points or one so one over X. It&#x27;s weird. It&#x27;s more than opening over what X is. Ah, it&#x27;s is negative, and X squared is positive. So from here we can say that there is a broken for that. So it&#x27;s square is bigger than one over open toe ones for excess bread. Bigger that one were open. One of these 100 so X is a smarter than negative square or 100 where it&#x27;s is negative. As we sit here, X is smaller than negative then so N is they get the there.

R M · Answer

problem number 47. Assume that X in the smaller than and negative five years to so up. Tributes off Negative 11 over two x bus fire, which is equal to or X minus one minus four x minus 10 over two X plus five is equal to or X minus one over, UH two X plus five minus two, which it&#x27;s mortar than four point 4.1. Ah, so here we can say that, and then that they live in over two x A plus five ah smaller than 4.1 where two X plus five is negative. Uh, sure, we can see that who X plus by over 11 is Ah, more than that. We&#x27;ll point you want one over open one Just negative 10. From here, we can say that X is smoother than negative 115 over to so, and it&#x27;s equal to negative 115

R M · Answer

a problem. Number 41. Ah, the limits. Ah, X stands stool, a positive infinity off one over X squared exist, and it&#x27;s equal to zero. I am using the definition one 0.4 point two for absolute equal toe 10 or negative, too. We can choose and which belongs to ends that that inequality off one over its square, minus zero. She gets equal to one over its Where is this mother than 10? Forward? Negative to. It&#x27;s satisfied for X. Bigger than so It&#x27;s fine. Inner ah, one over its word. Smaller than 10 or negative, too. So excess where is bigger than 10 square show X were absolute X is bigger than intent. So we set and is equal to in If we said anything 2010 in using the last result. Inequality. The absolute off one over, uh, one over X squared minus zero should be smaller. That important Negative. It&#x27;s a spy for X, bigger than n where n is

R M · Answer

problem Number 48. Assume that X is one of that negative one. So absolute over negative one X plus one, which can be a bit and as X minus X minus one over experts one which which can be written as X over. Expose one minus one in smaller than your point or what? So from here we can say that I get the one. Except this one, it&#x27;s wonder than what point or one where X A plus one is negative. So from these inequality, we can say that exit plus one. It&#x27;s smaller than negative 1/4 point one, which gets negative, some event so x smoother that negative, uh, what&#x27;s ocean and one so end it&#x27;s equal to negative oneself.

R M · Answer

problem Number 45. Assume that X is one of them. Negative tools weren&#x27;t over Exit plus two. It is one of that more point away. Five. So negative one over X plus two. It&#x27;s more than open or five, where X Plus two is negative. Ah, so, um, one over X plus two is bigger than negative, open or fine, so x A plus two is smaller than negative. One over ballpoint or five years negative. 200 so X It&#x27;s water than negative 100 to so we can say that n it&#x27;s negative.

R M · Answer

a Brooklyn number 43. The pope at X is a positive, so absolute over negative one over X Bus one, which is equal to X minus X minus one over X A plus one, which is equal toe It&#x27;s over. Exposed one minus one. It&#x27;s smaller than a funny one show for Ah one over X A plus one. It&#x27;s Warner than opening or one where experts when his mother so X plus one it&#x27;s bigger, bigger than 1/4 0.1 is equal to itself in S O X is bigger than 1999 so n is equal 119 and 999.

Problem

A positive number $\epsilon$ and the limit $L$ of…

Problem 46 Easy Difficulty

A positive number $\epsilon$ and the limit $L$ of a function $f$ at $-\infty$ are given. Find a negative number $N$ such that $|f(x)-L|<\epsilon$ if $x<N$.
$$\lim _{x \rightarrow-\infty} \frac{1}{x^{2}}=0 ; \epsilon=0.01$$

Answer

$|x|>10$

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Howard Anton, Irl Bivens, Stephen Davis

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$|x|>10$

Calculus Early Transcendentals

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Precalculus Review - Intro

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Howard Anton, Irl Bivens, Stephen DavisCalculus Early Transcendentals

Catherine R.

Heather Z.

Samuel H.

Michael J.

Howard Anton, Irl Bivens, Stephen Davis

Calculus Early Transcendentals