# How do you find the Vertical, Horizontal, and Oblique Asymptote given #g(x)= (x+2 )/( 2x^2)#?

The vertical asymptote is

No oblique asymptote.

The horizontal asymptote is

graph{(y-(x+2)/(2x^2))(y)(y-100x)=0 [-7.02, 7.024, -3.51, 3.51]}

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To find the vertical asymptote, set the denominator equal to zero and solve for x. In this case, 2x^2 = 0, which gives x = 0.

To find the horizontal asymptote, compare 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 degrees are equal, divide the leading coefficients of the numerator and denominator to find the horizontal asymptote. Here, since the degree of the numerator is 1 and the degree of the denominator is 2, the horizontal asymptote is y = 0.

To find the oblique asymptote, divide the numerator by the denominator using polynomial long division or synthetic division. In this case, g(x) = (x + 2)/(2x^2) simplifies to (1/2x) + (1/x^2). Since the degree of the numerator is less than the degree of the denominator, there is no oblique asymptote.

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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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- How do you find vertical, horizontal and oblique asymptotes for #[(3x^2) + 14x + 4] / [x+2]#?
- How do you find the vertical, horizontal and slant asymptotes of: #f(x) = (6x + 6) / (3x^2 + 1)#?

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