# How to find the asymptotes of #y = (7x-5)/(2-5x)# ?

Explanation is given below.

To find the vertical asymptote equate the denominator to zero.

For finding the Horizontal asymptotes, we start by comparing the degrees of the numerator and denominator.

If the degree of the numerator is greater than the degree of the denominator then there is no Horizontal Asymptote.

If the degree of the numerator equals the degree of the denominator then the horizontal asymptote is given by

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To find the asymptotes of ( y = \frac{7x - 5}{2 - 5x} ), follow these steps:

- Check for vertical asymptotes: Vertical asymptotes occur where the denominator equals zero, but the numerator does not. Set the denominator equal to zero and solve for ( x ).

[ 2 - 5x = 0 ] [ \Rightarrow 5x = 2 ] [ \Rightarrow x = \frac{2}{5} ]

So, there is a vertical asymptote at ( x = \frac{2}{5} ).

- Check for horizontal asymptotes: Horizontal asymptotes occur when ( x ) approaches positive or negative infinity. To find horizontal asymptotes, compare the degrees of the numerator and the denominator.

The degree of the numerator is 1, and the degree of the denominator is also 1. When the degrees are the same, the horizontal asymptote is the ratio of the leading coefficients.

Therefore, the horizontal asymptote is ( y = \frac{7}{-5} = -\frac{7}{5} ).

In summary, the asymptotes of ( y = \frac{7x - 5}{2 - 5x} ) are:

- Vertical asymptote: ( x = \frac{2}{5} )
- Horizontal asymptote: ( y = -\frac{7}{5} ).

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When evaluating a one-sided 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 one-sided 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 one-sided 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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