# How do you identify the vertical asymptotes of #f(x) =2/(x^2+3x-10)#?

Find the zeros of the denominator and make sure they are not also zeros of the numerator. (If any of them are: factor, reduce the quotient and try again.)

(For a quadratic equation, I always try factoring first, because it's fast. But don't spend a lot of time on factoring, because you can use the quadratic formula to get zeros.)

Obviously, neither of these numbers is a zero of the numerator so:

The vertical asymptotes are the lines whose equations are:

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To identify the vertical asymptotes of the function f(x) = 2/(x^2 + 3x - 10), we need to find the values of x that make the denominator equal to zero, since vertical asymptotes occur where the function is undefined.

To do this, we set the denominator equal to zero and solve for x: x^2 + 3x - 10 = 0

Next, we factor the quadratic equation: (x + 5)(x - 2) = 0

Then, we set each factor equal to zero and solve for x: x + 5 = 0 => x = -5 x - 2 = 0 => x = 2

So, the vertical asymptotes of the function f(x) = 2/(x^2 + 3x - 10) occur at x = -5 and x = 2.

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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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