How do you find the asymptotes for #y=(x3)/(2x+5)#?
Vertical Asymptote:
Horizontal Asymptote:
For the vertical asymptote:
For the horizontal asymptote:
Take the limit of the function
and therefore
graph{(y (x3)/(2x+5))(y1/2)=0[20,20,10,10]}
God bless....I hope the explanation is useful.
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To find the asymptotes of the rational function y = (x  3) / (2x + 5), you need to determine where the function approaches infinity or negative infinity.

Horizontal Asymptote:
 If the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is y = 0.
 If the degrees are equal, divide the leading coefficients to find the horizontal asymptote.
 If the degree of the numerator is greater than the degree of the denominator, there is no horizontal asymptote.

Vertical Asymptote:
 Set the denominator equal to zero and solve for x. The vertical asymptote(s) occur where the function is undefined due to division by zero.
For the given function y = (x  3) / (2x + 5):
 Degree of the numerator: 1
 Degree of the denominator: 1
 Leading coefficients: 1 for both numerator and denominator
Since the degrees are equal and the leading coefficients are also equal, divide the leading coefficients: Horizontal Asymptote: y = 1/2
For vertical asymptotes, set the denominator equal to zero and solve for x: 2x + 5 = 0 x = 5/2
So, the vertical asymptote is x = 5/2.
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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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