# What are the points of discontinuity and vertical asymptote #(x^2 - 2x - 8)/(x + 6)#?

Vertical asymptote x= -6 and point of discontinuity is at x= -6

Vertical asymptote is x= -6 and the function is discontinuous at x=-6, because , then it becomes undefined.

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The points of discontinuity for the function (x^2 - 2x - 8)/(x + 6) occur when the denominator, x + 6, equals zero. Therefore, the point of discontinuity is x = -6.

To find the vertical asymptote, we need to determine the behavior of the function as x approaches positive or negative infinity.

As x approaches positive or negative infinity, the function approaches the value of x^2/x, which simplifies to x. Therefore, the vertical asymptote is y = x.

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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 #(3x^2+20x)/(4x^2+9)# as x goes to infinity?

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