Homework Help

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

user profile pic

jmg5639 | Student, Undergraduate | Honors

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

dislike 0 like

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

Tagged with caculus, math

1 Answer | Add Yours

user profile pic

lfryerda | High School Teacher | (Level 2) Educator

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

dislike 0 like

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

`=-7+6`

`=-1`

The limit evaluates to -1.

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes