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(e^(x^2) - cos ax) over a product of standard forms

This type of question, asked 2 times: May 2021 S1, 26 Apr 2025 S2. All 2 questions below, oldest first.

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  1. Question 1

    May 2021 S1

    130
    lim⁡x→0ex2−cos⁡xx2\lim_{x\to0}\frac{e^{x^2}-\cos x}{x^2} is equal to

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  2. Question 2

    26 Apr 2025 S2

    109
    lim⁡x→0ex2−cos⁡3xsin⁡x log⁡(1+2x)=\lim_{x\rightarrow 0} \frac{e^{x^{2}}- \cos 3x}{\sin x\ \log(1 + 2x)}=

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