The largest value of the non-negative integer for which is

MATHEMATICS · Numerical · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

The largest value of the non-negative integer

a

for which

\lim_{x\to1}\left\{\frac{-ax+\sin(x-1)+a}{x+\sin(x-1)-1}\right\}^{\frac{1-x}{1-\sqrt{x}}}=\frac14