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How do you find the vertical, horizontal or slant asymptotes for #(x^2+4)/(6x-5x^2)#?

Answer 1

Lily Anderson

Horizontal asymptote of #-1/5#
No slant asymptotes
Vertical asymptotes are #x=1.2# and #x=0#

HA of #-1/5# because the degrees are the same in the denominator and numerator, so you divide the coefficients.

Since the numerator degree should be one greater than the denominator, which it is not, there are no slant asymptotes.

Vertical asymptotes are #x=1# and #x=5# because #6x-5x^2# factored is #(x-1.2)# and #(x)#

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Answer 2

Anna Allen

To find the vertical asymptotes of ( \frac{x^2 + 4}{6x - 5x^2} ), set the denominator equal to zero and solve for ( x ). There are no horizontal or slant asymptotes for this rational function.

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Answer from HIX Tutor

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.