How to find the oblique asymptote of root of a function? f(x)=sqrt(4x^2+x+6)

Ryder Ferguson

Ryder Ferguson

Answered question

2022-10-31

How to find the oblique asymptote of root of a function?
f ( x ) = 4 x 2 + x + 6

Answer & Explanation

Adenomacu

Adenomacu

Beginner2022-11-01Added 13 answers

Yes. If f has an oblique asymptote (call it y = a x + b), you will have:
a = lim x ± f ( x ) x
b = lim x ± f ( x ) a x
In your example, lim x + 4 x 2 + x + 6 x = 2 and lim x + 4 x 2 + x + 6 2 x = 1 4
The asymptote as x + is therefore y = 2 x + 1 4

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