# What are the points of discontinuity of #y =(x + 3)/((x - 4)(x + 3)#?

The discontinuity points are the zeroes of the denominator, so:

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It is continuous on its domain. (Every rational function iscontinuous on its domain.)

(The discontinuity at 4 is infinite and that at -3 is removable.)

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The point of discontinuity of the function y = (x + 3)/((x - 4)(x + 3)) is x = -3 and x = 4.

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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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- What is the limit of #(2x^2+3)^(1/2) - (2x^2-5)^(1/2)# as x approaches infinity?
- What is the limit of #sinx / x# as x goes to infinity?

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