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Evaluate the limit : `lim_(x->0) (18+7/x)`

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jjmgingrich | Student, Undergraduate | Salutatorian

Posted January 23, 2013 at 2:35 AM via web

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Evaluate the limit : `lim_(x->0) (18+7/x)`

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degeneratecircle | High School Teacher | (Level 2) Associate Educator

Posted January 23, 2013 at 3:52 AM (Answer #2)

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If `x` is a small positive number, then `7/x` and therefore `18+7/x` are both large positive numbers. However, if `x` is a small negative number, then `7/x` and therefore `18+7/x` are both large negative numbers. Expressed mathematically,

`lim_(x->0^+) (18+7/x)=oo,` but

`lim_(x->0^-)(18+7/x)=-oo.`

Therefore the limit does not exist.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted January 23, 2013 at 3:12 AM (Answer #1)

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The limit `lim_(x->0)18+7/x` has to be determined.

As `x->0` , `1/x->oo` .

This gives `lim_(x->0)18+7/x = 18 +oo = oo`

The limit `lim_(x->0)18+7/x = oo`

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