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Limit at infinity of a ratio of polynomials (leading coefficients)

This type of question, asked 3 times: 26 Apr 2025 S1, 15 Apr 2026 S2, 14 May 2026 S1. All 3 questions below, oldest first.

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  1. Question 1

    26 Apr 2025 S1

    140
    lim⁡x→∞(2x+1)50+(2x+2)50+(2x+3)50+...+(2x+100)50(2x)50+(10)50=\lim_{x\rightarrow \infty} \frac{(2x+ 1)^{50}+ (2x+ 2)^{50}+ (2x+ 3)^{50}+ ... + (2x+ 100)^{50}}{(2x)^{50}+ (10)^{50}}=

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  2. Question 2

    15 Apr 2026 S2

    62
    If lim⁡x→∞(2x−1)19⋅(3x+2)11(6x−5)30=2a⋅3b\displaystyle\lim_{x \to \infty}\dfrac{(2x - 1)^{19}\cdot(3x + 2)^{11}}{(6x - 5)^{30}} = 2^a \cdot 3^b, then a+b=a + b =

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  3. Question 3

    14 May 2026 S1

    62
    If f(x)=ax−35x+7f(x) = \dfrac{ax - 3}{5x + 7} and lim⁡x→0f(x)⋅lim⁡x→∞f(x)=3\lim_{x \to 0}f(x) \cdot \lim_{x \to \infty}f(x) = 3 then a=…a = \ldots

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