原式=limx→0 [2-(1+cosx)]/9x^2*limx→0 1/[(√2+√(1+cosx)],(分子有理化,sin3x~3x替换) =√2/4*limx→0 (1-cosx)/9x^2, =√2/4*limx→0 sinx/18x,(洛必塔法则求导), =√2/4*1/18 =√2/72.
