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Find a and b from a limit at infinity of a rational function minus (ax + b)

This type of question, asked 3 times: 9 May 2023 S1, 18 Apr 2026 S1, 14 May 2026 S2. All 3 questions below, oldest first.

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  1. Question 1

    9 May 2023 S1

    115
    If lim⁡x→∞(x2+x+1x+1−ax−b)=4\lim_{x\to\infty}\left(\frac{x^2+x+1}{x+1} - ax - b\right) = 4 then

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  2. Question 2

    18 Apr 2026 S1

    59
    If lim⁡x→∞[x2+x+1x+1−ax−b]=3\lim_{x \to \infty}\left[\dfrac{x^2 + x + 1}{x + 1} - ax - b\right] = 3, then a−b=a - b =...

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  3. Question 3

    14 May 2026 S2

    63
    If lim⁡x→∞[x3+1x2+1−(ax+b)]=2\displaystyle\lim_{x \to \infty}\left[\dfrac{x^3 + 1}{x^2 + 1} - (ax + b)\right] = 2 then

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