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How do you evaluate the limit #(x^2-25)/(x+5)# as x approaches #-5#?

Answer 1

Emma Aldridge

#lim_(x ->-5)(x^2 - 25)/(x + 5) = -10#

Start by eliminating through factorization:

#=lim_(x -> -5)(cancel((x + 5))(x - 5))/cancel(x + 5)#

#= -5 - 5#

#=-10#

Hopefully this helps!

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Answer 2

Christopher Agresta

To evaluate the limit of (x^2-25)/(x+5) as x approaches -5, we can substitute -5 into the expression. This gives us (-5^2-25)/(-5+5), which simplifies to (25-25)/0. Since we have a denominator of 0, the limit does not exist.

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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.