SOLUTION: Please explain how to find the horizontal and vertical asymptotes of these functions using limits. If I understand correctly, to find the vertical asymptote you set the numerator t

Algebra ->  Functions -> SOLUTION: Please explain how to find the horizontal and vertical asymptotes of these functions using limits. If I understand correctly, to find the vertical asymptote you set the numerator t      Log On


   

Question 1000931: Please explain how to find the horizontal and vertical asymptotes of these functions using limits. If I understand correctly, to find the vertical asymptote you set the numerator to zero and solve. And to find the horizontal asymptote you compare the exponents, if they are the same, use the fraction, if the numerator is larger it DNE, if the denominator is larger then it is zero. I understand that decent enough but throwing limits in there is confusing. How do you find vertical and horizontal asymptotes by using limits on these functions?
+f%28x%29+=+5+%2B+e%5E%28-x%5E2%29+
+f%28x%29+=+%28x%5E3-9x%2B4%29%2F%282x%5E3%2B6x%2B7%29+
+f%28x%29+=+%281%29%2F%28ln%282x%2B4%29%29+
+f%28x%29+=+%28x%5E2-3x-10%29%2F%28sqrt%28x%2B2%29%29+
Thank you
Answer by ikleyn(52770) About Me  (Show Source):
You can put this solution on YOUR website!
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If I understand correctly, to find the vertical asymptote you set the numerator to zero and solve.
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It is incorrect.

To find the vertical asymptote you set the  denominator  to zero and solve.

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f%28x%29 = 5+%2B+e%5E%28-x%5E2%29+.

No vertical asymptotes.
Horizontal asymptote  y = 5,  because  e%5E%28-x%5E2%29  tends to zero  when  x --> infinity.
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f%28x%29 = %28x%5E3-9x%2B4%29%2F%282x%5E3%2B6x%2B7%29+

Horizontal asymptotes  1%2F2  when x ---> infinity,
and  1%2F2  when x ---> -infinity.

Vertical asymptotes are there where the denominator is zero:  2x%5E3+%2B+6x+%2B+7 = 0.

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f%28x%29 = %281%29%2F%28ln%282x%2B4%29%29+

No horizontal asymptotes.

Vertical asymptote at  x = -1.5   (where  2x+4 = 1  and  ln(2x+4) = ln(1) = 0).

The function is defined at  x > -2   (where  2x+4 > 0).

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f%28x%29 = %28x%5E2-3x-10%29%2F%28sqrt%28x%2B2%29%29.

No horizontal asymptotes.

Vertical asymptote  x = -2   (where x+2 = 0).

The function is defined at  x > -2.