如图
4.
lim xⁿlnx
x→0
=lim lnx/x⁻ⁿ
x→0
=lim (1/x)/[(-n)x⁻ⁿ⁻¹]
x→0
=lim -xⁿ/n
x→0
=0
5.
∫[1/(a²+x²)]dx
=(1/a)∫d(x/a)/[1+(x/a)²]
=(1/a)arctan(x/a) +C
6.
令x=asint
x：0→a，则t：0→π/2
∫[0：a]√(a²-x²)dx
=∫[0：π/2]√(a²-a²sin²t)d(asint)
=a²∫[0：π/2]cos²tdt
=½a²∫[0：π/2](1+cos2t)dt
=½a²(t+½sin2t)|[0：π/2]
=½a²[(π/2 +½sinπ)-(0+½sin0)]
=½a²[(π/2 +0)-(0+0)]
=¼πa²
内容全部来源于网络收集，如有侵权，请联系网站删除：QQ：24596024