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How do you evaluate #(3e^-x+6)/(6e^-x+3)# as x approaches infinity?

Answer 1

Evelyn Agard

As #x->+oo# then #e^-x->0# hence the limit is

#lim_(x->+oo) (3*e^-x+6)/(6*e^-x+3)=6/3=2#

As #x->-oo# then #e^-x->oo# hence the limit is

#lim_(x->-oo) (3*e^-x+6)/(6*e^-x+3)=3/6=1/2#

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Answer 2

Christopher Allers

As x approaches infinity, the terms involving e^-x become negligible. Therefore, the expression can be simplified by ignoring those terms. Evaluating the simplified expression, we get 1/2.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.