What are the removable and non-removable discontinuities, if any, of #f(x)=(x^3 - x^2 - 72 x)/ (x - 9) #?

Answer 1

It has a removable singularity at #x=9#

We have:

# f(x)=(x^3 - x^2 - 72 x)/ (x - 9) #
Clearly when the denominator #x-9=0 => x=0# is the only singularity.

Let's see if we can remove it:

# f(x)=(x(x^2 - x - 72 ))/ (x - 9) # # " " =(x(x+8)(x-9))/ (x - 9) #
And so we can "cancel" the #(x-9)# factor and remove the singularity to give:
# f(x) =x(x+8) #
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Answer 2

The removable discontinuity of f(x) is at x = 9. There are no non-removable discontinuities.

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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.

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.

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.

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.

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