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How do you evaluate the limit #(x^2+4x+2)/(x^2-3)# as x approaches #-3#?

Answer 1

Ezra Adams

By substitution.

Since #lim_(xrarr-3)(x^2-3) != 0# we can simply find the quotient of the limits,

#lim_(xrarr-3)(x^2+4x+2)/(x^2-3) = (lim_(xrarr-3)(x^2+4x+2))/(lim_(xrarr-3)(x^2-3))#

# = ((-3)^2+4(-3)+2)/((-3)^2-3) = -1/6#

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Answer 2

Evelyn Agard

To evaluate the limit of (x^2+4x+2)/(x^2-3) as x approaches -3, we substitute -3 into the expression. This gives us (-3^2+4(-3)+2)/(-3^2-3). Simplifying further, we get (-9-12+2)/(-9-3), which equals -19/-12. Finally, simplifying the fraction gives us the answer of 19/12.

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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.