lim(x→0)[(1+xsinx)^1/2-1]/(sinx)^2=

来源：学生作业帮助网编辑：作业帮时间：2024/05/03 01:49:52

lim(x→0)[(1+xsinx)^1/2-1]/(sinx)^2=
lim(x→0)[(1+xsinx)^1/2-1]/(sinx)^2=

lim(x→0)[(1+xsinx)^1/2-1]/(sinx)^2=
lim(x→0) [√(1 + xsinx) - 1]/sin²x
= lim(x→0) [√(1 + xsinx) - 1]/x²、sinx x
= lim(x→0) [√(1 + xsinx) - 1]/x² * [√(1 + xsinx) + 1]/[√(1 + xsinx) + 1]
= lim(x→0) [(1 + xsinx) - 1]/[x²(√(1 + xsinx) + 1)]
= lim(x→0) xsinx/[x²(√(1 + xsinx)) + 1]、sinx x
= lim(x→0) x²/[x²(√(1 + xsinx)) + 1]
= lim(x→0) 1/[√(1 + xsinx) + 1]
= 1/[√(1 + 0) + 1]
= 1/2

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