Suppose ( _ x 0 _ 0 ^ x t^2 dt (a+t^r)^ 1/p bx - x = l )

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

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 (1) b>1b > 1 (2) 0<b<10 < b < 1 (3) b<0b < 0 (4) b=1b = 1

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