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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 $x<N$.
$$\lim _{x \rightarrow-\infty} \frac{1}{x+2}=0 ; \epsilon=0.005$$

R M · Accepted 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

remember 42 uh, limits off extents through positive sanity. Ah, one over X plus Q exist, and it&#x27;s equal to zero then, by using the definition, 1.4 point two for absolute is equal through fire times. 10. For negative three, we can choose n and such A that that inequality off one over X plus two minus zero is smaller than by time stamp or negative. Three. It&#x27;s a strike for Old X, bigger than then, so to find. And we have. And to say that from this inequality X plus two that&#x27;s appropriate for this inequality, it&#x27;s bigger than at them. For three Cooper Fine, which is 200 so X is bigger than 1 98 or X, is smaller than negative at 100 to. So we can said that N is equal to 203 then, using the last result inequality one over X, a plus to minus. Do you? It&#x27;s wonder that by times 10 or negative three is sets Freud for X bigger than in where n is two or three

R M · 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

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

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

Problem

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

Problem 45 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 $x<N$.
$$\lim _{x \rightarrow-\infty} \frac{1}{x+2}=0 ; \epsilon=0.005$$

Answer

-202

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Calculus Early Transcendentals

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Howard Anton, Irl Bivens, Stephen DavisCalculus Early Transcendentals

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Howard Anton, Irl Bivens, Stephen Davis

Calculus Early Transcendentals