How do you find the asymptotes for #(x^4  2x + 3) / (6  5x^3)#?
There is an asymptote where
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To find the asymptotes for ( \frac{{x^4  2x + 3}}{{6  5x^3}} ), we examine both horizontal and vertical asymptotes.

Vertical Asymptotes: Vertical asymptotes occur where the denominator of the rational function equals zero. Set the denominator ( 6  5x^3 ) equal to zero and solve for ( x ): [ 6  5x^3 = 0 ] [ 5x^3 = 6 ] [ x^3 = \frac{6}{5} ] [ x = \sqrt[3]{\frac{6}{5}} ]
Therefore, there is a vertical asymptote at ( x = \sqrt[3]{\frac{6}{5}} ).

Horizontal Asymptotes: To find horizontal asymptotes, we compare the degrees of the numerator and the denominator. Since the degree of the numerator (4) is greater than the degree of the denominator (3), there is no horizontal asymptote.
Thus, the asymptotes for the given rational function are:
 Vertical asymptote: ( x = \sqrt[3]{\frac{6}{5}} )
 There is no horizontal 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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