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  1. Identify the vertical asymptotes of

f(x) = 2/x^2+3x-10

  1. Identify the vertical asymptotes of f(x) = x+6/x^2-9x +18

  2. Identify the horizontal asymptote of f(x) =4x/7

  3. Identify the horizontal asymptote of f(x) = 7x+1/2x-9

5.Identify the horizontal asymptote of f(x) = x^2+5x-3/4x-1

  1. Identify the oblique asymptote of f(x) = x^2-4x+8 /x+2

7.Identify the oblique asymptote of f(x) = 2x^2+3x+8/x+3


8.Identify the oblique asymptote of f(x) = x+4/3x^2+5x-2

  1. Identify the oblique asymptote of

f(x) =4x^2-x+2/x

Verified Answer :

HomertheGenius
  1. x1/2=\(\frac{-3\pm \sqrt{9+40} }{2}\)
    VA(the vertical asymptotes): x=-5,  x=2
    2. x1/2=\(\frac{9\pm \sqrt{81-72} }{2}\)
    VA: x=3, x=6
    3.  \(\lim_{n \to \infty} \frac{4x}{7}\)=∞
    There is no HA.
    4. \(\lim_{n \to \infty} \frac{7x+1}{2x-9}= \frac{7}{9}\)
    HA : y=7/2
    5. \(\lim_{n \to \infty} \frac{ x^{2} +5x+3}{4x-1}\) =∞
    There is no HA.
    6. m=\(\lim_{n \to \infty} \frac{ x^{2} -4x+8}{ x^{2} +2x}\)
    m = 1
    b=\(\lim_{n \to \infty} \frac{ x^{2} -4x+8- x^{2} -2x}{x+2}\)
    b = -6
    OA: y = x - 6
    7. Same method:
    m = 2
    b = 0
    OA: y = 2x
    8. m = 0
    There is no OA.
    m = 4 
    b=-1
    OA: y=4x-1

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