How do you find vertical, horizontal and oblique asymptotes for #(x^2x+1)/(x3)#?
The vertical asymptote is
No horizontal asymptote.
The oblique asymptote is
Consequently,
Let's divide something long.
Consequently,
graph{(yx2)=0 [41.1, 41.1, 20.56, 20.56]} or y(x^2x+1)/(x3)
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To find vertical, horizontal, and oblique asymptotes for the function (\frac{x^2x+1}{x3}):

Vertical asymptotes: Set the denominator equal to zero and solve for (x). The values of (x) obtained will give the vertical asymptotes. [x  3 = 0] [x = 3]

Horizontal asymptotes: 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. In this case, the degree of the numerator (2) is greater than the degree of the denominator (1), so there is no horizontal asymptote.

Oblique asymptotes: If the degree of the numerator is exactly one more than the degree of the denominator, divide the numerator by the denominator using long division or synthetic division to find the equation of the oblique asymptote. [x^2  x + 1 = (x  3)(x + 2)  5] So, the oblique asymptote is (y = x + 2).
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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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