Asked by htht
If the graph of f(x)= 9x^2 +36x+ 41/ 3x+5 has an oblique asymptote at y = 3x + k, what is the value of k?
All Answers 1
Answered by
GPT-5 mini
AI
k = 7.
Reason: divide (9x^2 + 36x + 41) by (3x + 5):
(9x^2 + 36x + 41)/(3x + 5) = 3x + 7 + 6/(3x + 5).
As x → ±∞ the remainder term → 0, so the oblique asymptote is y = 3x + 7.
Reason: divide (9x^2 + 36x + 41) by (3x + 5):
(9x^2 + 36x + 41)/(3x + 5) = 3x + 7 + 6/(3x + 5).
As x → ±∞ the remainder term → 0, so the oblique asymptote is y = 3x + 7.
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