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How do you evaluate the limit of #lim (x+2)/(x^2-4)# as #x->-2#?

Answer 1

Cora Alexander

Factor the denominator and cancel like factors or use L'Hôpital's rule ; either way works.

#lim_(xto-2)(x + 2)/(x^2 - 4)#

Factor the denominator:

#lim_(xto-2)(x + 2)/((x - 2)(x + 2))#

Cancel common factors:

#lim_(xto-2)cancel(x + 2)/((x - 2)cancel(x + 2))#

Evaluate at the limit.

#lim_(xto-2)1/(x - 2) = 1/(-2 - 2) = -1/4#

Use L'Hôpital's rule

The derivative of the numerator:

#(d(x + 2))/dx = 1#

The derivative of the denominator:

#(d(x^2 - 4))/dx = 2x#

#lim_(xto-2) 1/2x = 1/(2(-2)) = -1/4#

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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.

How do you evaluate the limit of #lim (x+2)/(x^2-4)# as #x-&gt;-2#?

How do you evaluate the limit of #lim (x+2)/(x^2-4)# as #x->-2#?