How do you find the asymptotes for # y= (x+1)^2 / ((x1)(x3))#?
Vertical Asymptotes:
Horizontal asymptotes:
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To find the asymptotes of the rational function ( y = \frac{(x+1)^2}{(x1)(x3)} ), we examine the behavior of the function as ( x ) approaches the vertical asymptotes and horizontal asymptotes:

Vertical Asymptotes: Vertical asymptotes occur where the denominator of the rational function becomes zero, but the numerator does not. Set the denominator equal to zero and solve for ( x ). [ (x  1)(x  3) = 0 ] [ x = 1 \quad \text{and} \quad x = 3 ] So, there are vertical asymptotes at ( x = 1 ) and ( x = 3 ).

Horizontal Asymptotes: Horizontal asymptotes occur when the degree of the numerator is less than or equal to the degree of the denominator. The degree of the numerator is ( 2 ) and the degree of the denominator is ( 2 + 1 = 3 ). Thus, there is no horizontal asymptote.
Therefore, the vertical asymptotes of the function ( y = \frac{(x+1)^2}{(x1)(x3)} ) are at ( x = 1 ) and ( x = 3 ), and 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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