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How do you evaluate the limit #abs(x+1)+3/x# as x approaches -3?

Answer 1

Ezekiel Alexander

The function is continuous in #x=-3#, so the limit equals the value

#f(x)_(x=-3) = |-3+1|+3/(-3)= |-2|-1=2-1=1#

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Answer 2

Charles Anctil

To evaluate the limit of abs(x+1)+3/x as x approaches -3, we substitute -3 into the expression. This gives us abs((-3)+1)+3/(-3). Simplifying further, we have abs(-2)+3/(-3). Since the absolute value of -2 is 2, the expression becomes 2+3/(-3). Evaluating this, we get 2-1 = 1. Therefore, the limit of abs(x+1)+3/x as x approaches -3 is equal to 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.