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sin(pi cos^2 x)/x^2 as x tends to 0

The same question, asked 2 times: 2 May 2023 S2*, 25 Apr 2025 S1. Every wording below, oldest first.

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  1. Question 1

    2 May 2023 S2

    149
    lim⁡x→0sin⁡(πcos⁡2x)x2\lim_{x\to0}\frac{\sin(\pi\cos^2 x)}{x^2} is equal to

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  2. Question 2

    25 Apr 2025 S1

    128
    If f(x)=sin⁡(πcos⁡2x)3x2,x≠0f(x) =\frac{\sin\left( \pi\cos^{2}x \right)}{3x^{2}},x\neq 0 is continuous at x=0x= 0 then f(0)=f(0) =

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