求极限:lim(n→∞)2^nsinx/2^n(x不为零的常数);lim(x→0)(tanx-sinx)/x^3 ;lim(x→a)(sinx-sina)/(x-alim(x→π/3)sin(x-π/3)/(1-2cosx) 希望写写过程,
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/02 02:26:04
![求极限:lim(n→∞)2^nsinx/2^n(x不为零的常数);lim(x→0)(tanx-sinx)/x^3 ;lim(x→a)(sinx-sina)/(x-alim(x→π/3)sin(x-π/3)/(1-2cosx) 希望写写过程,](/uploads/image/z/1615664-56-4.jpg?t=%E6%B1%82%E6%9E%81%E9%99%90%3Alim%EF%BC%88n%E2%86%92%E2%88%9E%292%5Ensinx%2F2%5En%28x%E4%B8%8D%E4%B8%BA%E9%9B%B6%E7%9A%84%E5%B8%B8%E6%95%B0%EF%BC%89%EF%BC%9Blim%28x%E2%86%920%29%28tanx-sinx%29%2Fx%5E3+%EF%BC%9Blim%28x%E2%86%92a%29%28sinx-sina%29%2F%28x-alim%28x%E2%86%92%CF%80%2F3%29sin%28x-%CF%80%2F3%29%2F%281-2cosx%29+%E5%B8%8C%E6%9C%9B%E5%86%99%E5%86%99%E8%BF%87%E7%A8%8B%2C)
求极限:lim(n→∞)2^nsinx/2^n(x不为零的常数);lim(x→0)(tanx-sinx)/x^3 ;lim(x→a)(sinx-sina)/(x-alim(x→π/3)sin(x-π/3)/(1-2cosx) 希望写写过程,
求极限:lim(n→∞)2^nsinx/2^n(x不为零的常数);lim(x→0)(tanx-sinx)/x^3 ;lim(x→a)(sinx-sina)/(x-a
lim(x→π/3)sin(x-π/3)/(1-2cosx) 希望写写过程,
求极限:lim(n→∞)2^nsinx/2^n(x不为零的常数);lim(x→0)(tanx-sinx)/x^3 ;lim(x→a)(sinx-sina)/(x-alim(x→π/3)sin(x-π/3)/(1-2cosx) 希望写写过程,
①等价无穷小量替换:
lim(n→∞)2^nsin(x/2^n)
=lim(n→∞)2^n*(x/2^n)
= x
②
【罗必塔法则】
lim(x→0)(tanx-sinx)/x^3
=lim(x→0)(sec^2 x - cosx)/3x^2
=lim(x→0)(2sec^2 xtanx + sinx)/6x
=lim(x→0)(2sec^2 x/cosx + 1)*sinx/6x
= 3*(1/6)
= 1/2
③
lim(x->a) [sinx - sina]/[x-a]
=lim(x->a) { 2cos[(x+a)/2][sin(x-a)/2] }/ [x-a]
=lim(x->a) cos[(x+a)/2]* {2[(x-a)/2}/[x-a]
=cosa
④
【罗必塔法则】
lim(x→π/3)sin(x-π/3)/(1-2cosx)
=lim(x→π/3) cos(x-π/3)/2sinx
= 1/(2*1/2)
= 1