nynw.net
当前位置:首页 >> lim x→0 1%Cos4x/xsinx= >>

lim x→0 1%Cos4x/xsinx=

(x→0) lim (1-cos4x)/(xsinx) = (x→0) lim 2sin²(2x)/(xsinx) = (x→0) lim 2sin(2x)*2sinxcosx/(xsinx) = (x→0) lim 4sin(2x)*cosx/x = (x→0) lim 8cosx *sin(2x)/(2x) = 8*cos0*1 = 8

(x→0) lim (1-cos4x)/(xsinx) = (x→0) lim 2sin²(2x)/(xsinx) = (x→0) lim 2sin(2x)*2sinxcosx/(xsinx) = (x→0) lim 4sin(2x)*cosx/x = (x→0) lim 8cosx *sin(2x)/(2x) = 8*cos0*1 = 8

等价无穷小 1-cos4x~1/2*(4x)^2=8x^2 xsinx~x^2 原式=8

有理化不清楚什么意思

lim(x→0)[e^sinx-e^tanx]/[x(1-cos4x)] x->0 sinx ~ x -(1/6)x^3 e^sinx ~ 1 + (x -(1/6)x^3) + (x -(1/6)x^3)^2/4 ~ 1+x +x^2/4 -(1/6)x^3 tanx ~ x + (1/3)x^3 e^tanx ~1 + (x +(1/3)x^3) + (x +(1/3)x^3)^2/4 ~ 1+x +x^2/4 +(1/3)x^3 e^sinx...

x→0 lim (1-cos4x) / (x*sinx) 因为,cos4x=1-2sin^2(2x) =lim 2sin^2(2x) / (x*sinx) 上下同时除以x^2 =lim 2sin^2(2x)/x^2 / (x*sinx)/x^2 =lim 8sin^2(2x)/4x^2 / (x*sinx)/x^2 =lim 8*sin^2(2x)/(2x)^2 / (sinx/x) =lim 8*sin^2(2x)/(2x)^2 ...

x→0时 原式=lim(x→0)(-sinx+4sin4x)/2x =lim(x→0)(-cosx+16cos4x)/2 =(-1+16)/2 =15/2

∫ 1/(sinxcos⁴x) dx = ∫ cscxsec⁴x dx = ∫ cscx(1 + tan²x)² dx = ∫ cscx(1 + 2tan²x + tan⁴x) dx = ∫ (cscx + 2secxtanx + secxtan³x) dx = ∫ cscx dx + 2∫ secxtanx dx + ∫ secxtanx(sec²x - 1) d...

如果没学习洛比达法则, (secx)²-2tanx=(tanx)²+1-2tanx=(tanx-1)²=(1/cosx)²(sinx-cosx)² 1+cos4x=2(cos2x)²-1+1=2(cos2x)²=2[(cosx)²-(sinx)²]²=2(cosx-sinx)²(cosx+sinx)² 所以...

1. lim (sinx+cos2x)/(x+1)=0 x→∞ 解题思路:有界/无穷大=0 2、 lim [1-3/(4x)]^(2x) x→∞ lim {[1-3/(4x)]^(-4x/3)}^(-3/2) x→∞ =e^(-3/2) 用到的公式: lim (1+ 1/x)^x=e x→∞

网站首页 | 网站地图
All rights reserved Powered by www.nynw.net
copyright ©right 2010-2021。
内容来自网络,如有侵犯请联系客服。zhit325@qq.com