How do you find the Vertical, Horizontal, and Oblique Asymptote given #y = (2x+4)/( x^23x4)#?
so we have vertical asymptotes at
for horizontal and slope asmptotes,
for vertical aympptotes, we look at when the demoninator is zero
so
to check for possible indeterminates we note that
and
so we have vertical asymptotes at
for horizontal and slope we look at the behaviour of the function as
so we rewrite
as
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To find the vertical, horizontal, and oblique asymptotes of the function (y = \frac{2x + 4}{x^2  3x  4}), follow these steps:

Vertical Asymptotes: Vertical asymptotes occur where the denominator of the function is equal to zero, but the numerator is not zero. Set the denominator (x^2  3x  4) equal to zero and solve for (x) to find the vertical asymptotes.

Horizontal Asymptotes: Horizontal asymptotes occur when (x) approaches positive or negative infinity. To find horizontal asymptotes, examine the degrees of the numerator and denominator. If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y = 0. If the degree of the numerator is equal to the degree of the denominator, divide the leading coefficients to find the horizontal asymptote. If the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote.

Oblique Asymptotes: Oblique (slant) asymptotes occur when the degree of the numerator is exactly one greater than the degree of the denominator. To find the oblique asymptote, perform polynomial long division or use another method to divide the numerator by the denominator. The quotient represents the equation of the oblique asymptote.
Following these steps will help you determine the vertical, horizontal, and oblique asymptotes for the given function.
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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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