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NeTakaya
3 years ago
12

Find Horizontal and Vertical asymptotes for y=(x^2 -9)/(4x^2 +1)

Mathematics
1 answer:
Gnom [1K]3 years ago
8 0

Answer: Horizontal asymptote is \dfrac{1}{4} and vertical asymptotes are \pm \dfrac{1}{2i}

Step-by-step explanation:

Since we have given that

y=\dfrac{x^2-9}{4x^2+1}

We need to find the horizontal and vertical asymptotes.

Since vertical asymptotes will occur where the denominator becomes zero.

So, here denominator is 4x^2+1

Now,

4x^2+1=0\\\\4x^2=-1\\\\x^2=\dfrac{-1}{4}\\\\x=\pm \dfrac{1}{2i}

And the horizontal asympototes will occur when the coefficient of higher degree of numerator is divided by coefficient of higher degree of denominator.

y=\dfrac{1}{4}

Hence, horizontal asymptote is \dfrac{1}{4} and vertical asymptotes are \pm \dfrac{1}{2i}

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