数学极限lim(x→0)(tan2x
这里只用重要极限：lim(x→0)(sinx)/x=1求解。
1。lim(x→0) (tan2x-sinx)/x
=lim(x→0) (sin2x/cos2x-sinx)/x
=lim(x→0) (2sinxcosx/cos2x-sinx)/x
=lim(x→0) [(sinx)/x]*(2cosx/cos2x-1)
=1*(2/1-1)
=1。
2。lim(x→0) (tanx-sinx)/(sinx)^3
=lim(x→0) (1/cosx-1)/(sinx)^2
=lim(x→0) (1-cosx)/[cosx(sinx)^2]
=lim(x→0) 2[sin(x/2)]^2/[...全部
这里只用重要极限：lim(x→0)(sinx)/x=1求解。
1。lim(x→0) (tan2x-sinx)/x
=lim(x→0) (sin2x/cos2x-sinx)/x
=lim(x→0) (2sinxcosx/cos2x-sinx)/x
=lim(x→0) [(sinx)/x]*(2cosx/cos2x-1)
=1*(2/1-1)
=1。
2。lim(x→0) (tanx-sinx)/(sinx)^3
=lim(x→0) (1/cosx-1)/(sinx)^2
=lim(x→0) (1-cosx)/[cosx(sinx)^2]
=lim(x→0) 2[sin(x/2)]^2/[cosx(sinx)^2]
=(1/2)lim(x→0) {[sin(x/2)]/(x/2)^2}^2*{1/[(sinx)/x]^2}*1/cosx
=(1/2)*1^2*{1/1^2}*1/1
=1/2。
。收起
