How do you find the slant asymptote of #y=(x^3)/((x^2)3)#?
The slant asymptote is:
Given:
Note that:
and:
So:
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To find the slant asymptote of the function ( y = \frac{x^3}{x^2  3} ), follow these steps:

Perform polynomial long division to divide ( x^3 ) by ( x^2  3 ). This gives you the quotient and remainder.

The quotient obtained from the division is the equation of the slant asymptote.
Let's perform the division:
[ \frac{x^3}{x^2  3} ]
[ = x \times \frac{x^2}{x^2  3} ]
[ = x \times \left(1 + \frac{3}{x^2  3}\right) ]
Now, divide ( x^2 ) by ( x^2  3 ):
[ = x \times \left(1 + \frac{3}{x^2  3}\right) ]
[ = x + \frac{3x}{x^2  3} ]
The quotient of the division is ( x + \frac{3x}{x^2  3} ), which represents the equation of the slant asymptote.
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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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