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How do you find the limit of # (X^2 – x – 6) / (X^2 – 5x + 6)# as x approaches 0?

Answer 1

Luke Alvarez

As #xrarr0#, the denominator approaches #6#. The form is not indeterminate.

As #xrarr0#, the numerator approaches #-6#.

So,

#lim_(xrarr0)(x^2-5-6)/(x^2-5x+6) = (-6)/6 = -1#

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Answer 2

Evelyn Agard

To find the limit of (x^2 – x – 6) / (x^2 – 5x + 6) as x approaches 0, we can substitute 0 into the expression and simplify. By doing so, we get (-6) / (6), which simplifies to -1. Therefore, the limit of the given expression as x approaches 0 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.