How do you find the asymptotes for #(3x2) / (x+1) #?
There are three kinds of asymptotes:
As for the horizontal ones, we have that
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To find the asymptotes of the function ( \frac{3x2}{x+1} ), you need to check for vertical and horizontal asymptotes.

Vertical Asymptote: Set the denominator equal to zero and solve for ( x ). Any ( x ) value that makes the denominator zero will result in a vertical asymptote.
( x + 1 = 0 ) ( x = 1 )
Therefore, ( x = 1 ) is the vertical asymptote.

Horizontal Asymptote: Compare the degrees of the numerator and denominator polynomial functions.
If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is at ( y = 0 ). If the degree of the numerator equals the degree of the denominator, divide the leading coefficients to find the horizontal asymptote.
Here, the degree of the numerator (1) is less than the degree of the denominator (1). So, the horizontal asymptote is ( y = 0 ).
Therefore, the vertical asymptote is ( x = 1 ) and the horizontal asymptote is ( y = 0 ).
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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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