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

Answer 1

# lim_(x rarr 3) -(x^2-3x)/(x-3) = -3 #

# lim_(x rarr 3) -(x^2-3x)/(x-3) = lim_(x rarr 3) -(x(x-3))/(x-3) # # lim_(x rarr 3) -(x^2-3x)/(x-3) = lim_(x rarr 3) (-x) # # lim_(x rarr 3) -(x^2-3x)/(x-3) = -3 #

Which we can confirm graphically; graph{-(x^2-3x)/(x-3) [-10, 10, -5, 5]}

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Answer 2

Christopher Allers

To evaluate the limit -(x^2-3x)/(x-3) as x approaches 3, we can substitute the value of 3 into the expression. However, this would result in an undefined expression since it would involve division by zero. To overcome this, we can simplify the expression by factoring the numerator. Factoring x^2-3x gives us x(x-3), which cancels out with the denominator (x-3). Therefore, the simplified expression becomes -x. Now, we can substitute the value of 3 into the simplified expression, which gives us -3 as the limit.

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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.