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Is the function f(x) = x^2 + 1/x^3 +1 continous at x = -1

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steve1234 | Student, Undergraduate | Salutatorian

Posted September 11, 2013 at 4:53 PM via web

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Is the function f(x) = x^2 + 1/x^3 +1 continous at x = -1

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted September 11, 2013 at 4:59 PM (Answer #1)

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The function `f(x) = (x^2 + 1)/(x^3 + 1)` . For a function f(x) to be continuous at x = a, f(a) should be defined, `lim(x->a) f(x)` should exist and `lim_(x->a) = f(a)` .

For `f(x) = (x^2 + 1)/(x^3 + 1)`

f(-1) = `(1 + 1)/(-1 + 1) = 2/0` which is not defined.

As a result `f(x) = (x^2 + 1)/(x^3 + 1)` is not continuous at x = -1.

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