Mathematics

Mathematics

Problem

Suppose lim⁡x→0∫0xt2dt(a+tr)1/pbx−sin⁡x=l\lim_{x \to 0} \frac{\int_{0}^{x} \frac{t^2 dt}{(a+t^r)^{1/p}}}{bx - \sin x} = l, where p∈N,p≥2,a>0,r>0p \in \mathbb{N}, p \ge 2, a > 0, r > 0 and b≠0b \ne 0. If ll exists and is non-zero, then a. b>1b > 1 b. 0<b<10 < b < 1 c. b<0b < 0 d. b=1b = 1

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