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What is # lim_(x->-oo) x^2/(x^2-7) #?

Answer 1

Emma Aldridge

#1#

We can divide both numerator and denominator by #x^2:#

#lim_(x->-oo)((cancel(x^2))/(cancel(x^2)))/(cancel(x^2)/cancel(x^2)-7/x^2)#

#=lim_(x->-oo)1/(1-7/x^2)=1/(1-7/(-oo)^2)=1#

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Answer 2

Charles Arocha

The limit of x^2/(x^2-7) as x approaches negative infinity is 1.

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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.

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What is # lim_(x-&gt;-oo) x^2/(x^2-7) #?

What is # lim_(x->-oo) x^2/(x^2-7) #?