What is the limit of # (t^2 - 64) / (2t^2 + 17 t + 8)# as t approaches -8?

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Answer 1 · 2016-09-24T20:38:01

Factor both the numerator and the denominator to see what you can eliminate.

#=>lim_(t -> -8) ((t + 8)(t - 8))/((2t^2 + 16t + t + 8))#

#=>lim_(t->-8) ((t + 8)(t - 8))/((2t(t + 8) + 1(t + 8))#

#=>lim_(t->-8) ((t + 8)(t - 8))/((2t + 1)(t + 8))#

#=>lim_(t->-8) (t - 8)/(2t + 1)#

#=> (-8 - 8)/(2 xx -8+ 1)#

#=>-16/-15#

#=>16/15#

Hopefully this helps!