How do you evaluate the limit $\frac{x}{x + 3}$ $x/(x+3)$ as x approaches $- 3$ $-3$ ?

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Answer 1 · 2016-09-19T18:03:00

The limit does not exist.

As $x \to - 3$ $xrarr-3$ , the numerator is negative.

the denominator is negative or positive and goes to $0$ $0$ (depending on whether $x$ $x$ goes to $- 3$ $-3$ from the left or from the right.

$lim_(xrarr-3^-) x/(x+3) = (-3)/(0^-) = oo$

$lim_(xrarr-3^+) x/(x+3) = (-3)/(0^+) = - oo$

$lim_(xrarr-3) x/(x+3)$ $" "$ Does Not Exist

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