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Evaluate the limit: `lim_{x->-7}{x^2+13x+42}/{x+7}` 

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jmg5639 | Student, Undergraduate | (Level 1) Honors

Posted January 22, 2013 at 1:26 AM via web

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Evaluate the limit: `lim_{x->-7}{x^2+13x+42}/{x+7}` 

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lfryerda | High School Teacher | (Level 2) Educator

Posted January 22, 2013 at 1:51 AM (Answer #1)

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To evaluate this limit, we see that with direct substitution the limit is 0/0, which means that we need to use another method.

In this case, factoring is needed.

`lim_{x->-7}{x^2+13x+42}/{x+7}`   factor the numerator

`=lim_{x->-7}{(x+6)(x+7)}/{x+7}`   cancel the common factors

`=lim_{x->-7}(x+6)`   sub in the value



The limit evaluates to -1.

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