Let f(x) = 3(x^4+x^3+x^2+1)/(x^2+x-2). Give a polynomial g(x) so that f(x) + g(x) has a horizontal asymptote of 0 as x approaches positive infinity.
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If you could give me the answer to this question quickly, that would be very helpful. Thanks!
+118691 I think that there is something wrong with your question.
That division has a remainder .....
+33652 "Let f(x) = 3(x^4+x^3+x^2+1)/(x^2+x-2). Give a polynomial g(x) so that f(x) + g(x) has a horizontal asymptote of 0 as x approaches positive infinity."
+118691 But Alan
3(x^4+x^3+x^2+1)/(x^2+x-2)
does not divide to give a polynomial so how can you say that this question makes sense. ?
+33652 The question doesn’t say that f(x) is a polynomial; it just asks for g(x) to be a polynomial, and for the limit of the sum of the two functions to have a zero asymptote.
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+118691
Well it doesn't make sense to me, it says that division gives a polynomial g(x)
"Let f(x) = 3(x^4+x^3+x^2+1)/(x^2+x-2). Give a polynomial g(x) so that f(x) + g(x) has a horizontal asymptote of 0 as x approaches positive infinity."
Was this the intended question?
Let f(x) = 3(x^4+x^3+x^2+1)/(x^2+x-2).
Find a polynomial g(x) such that f(x) + g(x) has a horizontal asymptote of 0 as x approaches positive infinity.
+33652 I don’t think it says division gives a polynomial Melody! There is a full stop (period) between the function definition and the word Give (which also starts with a capital letter), so I interpreted the sentence beginning with Give as an instruction to the reader, not a continuation of the previous sentence.
