# How do you find the asymptotes for #h(x)= (x^2-4)/(x)#?

oblique asymptote y = x

The first step is to divide out.

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To find the asymptotes of the function ( h(x) = \frac{x^2 - 4}{x} ), we need to check for vertical and horizontal asymptotes separately.

Vertical asymptotes occur where the denominator equals zero, but the numerator does not. So, set the denominator equal to zero and solve for ( x ).

[ x = 0 ]

This gives us the vertical asymptote ( x = 0 ).

Horizontal asymptotes are found by examining the behavior of the function as ( x ) approaches positive or negative infinity.

[ \lim_{x \to \pm \infty} h(x) = \lim_{x \to \pm \infty} \frac{x^2 - 4}{x} ]

By dividing the leading terms, we get:

[ \lim_{x \to \pm \infty} h(x) = \lim_{x \to \pm \infty} \frac{x^2}{x} = \lim_{x \to \pm \infty} x = \pm \infty ]

Therefore, there are no horizontal asymptotes for this function.

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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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