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(k/x^n)[1 - cos(x/2) - cos(x/4) + cos(x/2) cos(x/4)] as x tends to 0

The same question, asked 2 times: 10 May 2024 S2*, 19 Apr 2026 S1. Every wording below, oldest first.

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  1. Question 1

    10 May 2024 S2

    133
    If f(x)=4x4 ⁣[1−cos⁡x2−cos⁡x4+cos⁡x2⋅cos⁡x4]f(x)=\dfrac{4}{x^4}\!\left[1 - \cos\dfrac{x}{2} - \cos\dfrac{x}{4} + \cos\dfrac{x}{2}\cdot\cos\dfrac{x}{4}\right] is continuous at x=0x=0, then f(0)f(0) is

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  2. Question 2

    19 Apr 2026 S1

    61
    The value of lim⁡x→0(8x8)[1−cos⁡x22−cos⁡x24+cos⁡x22⋅cos⁡x24]\lim_{x \to 0}\left(\dfrac{8}{x^8}\right)\left[1 - \cos\dfrac{x^2}{2} - \cos\dfrac{x^2}{4} + \cos\dfrac{x^2}{2} \cdot \cos\dfrac{x^2}{4}\right] is equal to ...

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