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Q43Section C (Section C)43 of 60

Limit of integral ratio

Let α\alpha and β\beta be real constants such that lim⁡x→0+∫0x(αt21+t4) dtβx−sin⁡x=1.\lim_{x\to 0^+} \frac{\int_0^x \left(\frac{\alpha t^2}{1+t^4}\right)\,dt}{\beta x - \sin x} = 1. Then, the value of α+β\alpha+\beta equals __________

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