(x-arcsinx) / x ^ 2sin3x take the limit at x = 0

(x-arcsinx) / x ^ 2sin3x take the limit at x = 0

Equivalent Infinitesimal Substitution, sin3x is equivalent to 3x
The original formula = Lim [x → 0] (x-arcsinx) / (3x & # 179;)
Law of lobida
=lim[x→0] [1-1/√(1-x²)]/(9x²)
=lim[x→0] [√(1-x²)-1]/[9x²√(1-x²)]
Equivalent Infinitesimal Substitution: (1 + x) ^ A-1 is equivalent to ax, so √ (1-x & # 178;) - 1 = (1-x & # 178;) ^ (1 / 2) - 1 is equivalent to - (1 / 2) x & # 178;
=lim[x→0] [-(1/2)x²]/[9x²√(1-x²)]
=-1/18
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