lim(x→0)[(1+xsinx)^1/2-1]/(sinx)^2=
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lim(x→0)[(1+xsinx)^1/2-1]/(sinx)^2=
![lim(x→0)[(1+xsinx)^1/2-1]/(sinx)^2=](/uploads/image/z/10631334-30-4.jpg?t=lim%28x%E2%86%920%29%5B%281%2Bxsinx%29%5E1%2F2-1%5D%2F%28sinx%29%5E2%3D)
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
= 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
lim(x→0)[(1+xsinx)^1/2-1]/(sinx)^2=
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