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lim(x→0)f(x)/g(x)=1
左边=lim(x→0)sin(asin^2(x))*cosx/(3x^2+4x^3) (洛必达法则)
=lim(x→0)asin^2(x)/(3x^2+4x^3) (sinx~x, lim(x→0)cosx=1)
=lim(x→0)ax^2/(3x^2+4x^3) (sinx~x)
=lim(x→0)a/(3+4x)
=a/3
所以a=3
左边=lim(x→0)sin(asin^2(x))*cosx/(3x^2+4x^3) (洛必达法则)
=lim(x→0)asin^2(x)/(3x^2+4x^3) (sinx~x, lim(x→0)cosx=1)
=lim(x→0)ax^2/(3x^2+4x^3) (sinx~x)
=lim(x→0)a/(3+4x)
=a/3
所以a=3
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