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 2 years ago
Find all discontinuities of f(x). For each discontinuity that is removable, define a new function that removes the discontinuity. f(x) = x  1/x^2  1
 2 years ago
Find all discontinuities of f(x). For each discontinuity that is removable, define a new function that removes the discontinuity. f(x) = x  1/x^2  1

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tkhunny
 2 years ago
Best ResponseYou've already chosen the best response.0First, please remember your Order of Operations. You have NOT written \(\dfrac{x1}{x^{2}1}\). Give it another go and use more parentheses. Denominator = 0  Discontinuity. Is it an Asymptote or NonRemovable Discoutinuity? Numerator = 0 AT THE SAME PLACE, this it's Removable and NOT an Asymptote.

tkhunny
 2 years ago
Best ResponseYou've already chosen the best response.0?? There are two. 1) Which one are you talking about. 2) What's the other one?

onegirl
 2 years ago
Best ResponseYou've already chosen the best response.0removable discontinuity or infinite

onegirl
 2 years ago
Best ResponseYou've already chosen the best response.0so it will be replacing 0 will give you discontity right? and not any other number?

tkhunny
 2 years ago
Best ResponseYou've already chosen the best response.0Please make a better effort to use complete sentences and to be substantially more clear. I'll do a quick example. Sentences, paragraphs, examples, order. Working with the Denominator: \(x^{2}  1 = (x+1)(x1)\) This denominator takes on the value zero at x = 1 and x = 1. These values are NOT in the Domain and are discontinuities. We do not yet know what kind of discontinuity. Working with the Numerator x  1 = 0 when x = 1 This is enough information. x = 1 makes both Numerator and Denominator zero. This is, therefore, a removable discontinuity. Our original expression is equivalent to 1/(x+1) everywhere EXCEPT x = 1. x = 1 makes only the denominator zero. This is, therefore, an asymptote or infinite discontinuity. Now, we are done.
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