limx→0((✔1 tanx)-(✔sinx 1))/x^3求极限
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/02 02:12:38
![limx→0((✔1 tanx)-(✔sinx 1))/x^3求极限](/uploads/image/z/5616040-40-0.jpg?t=limx%E2%86%920%28%28%26%2310004%3B1+tanx%29-%28%26%2310004%3Bsinx+1%29%29%2Fx%5E3%E6%B1%82%E6%9E%81%E9%99%90)
limx→0((✔1 tanx)-(✔sinx 1))/x^3求极限
limx→0((✔1 tanx)-(✔sinx 1))/x^3
求极限
limx→0((✔1 tanx)-(✔sinx 1))/x^3求极限
lim(x->0)[√(1+tanx)- √(sinx+1) ]/x^3
=(1/2)lim(x->0)(tanx - sinx)/(x^3) (0/0)
=(1/2)lim(x->0)((secx)^2 - cosx)/(3x^2) (0/0)
=(1/2)lim(x->0)(2(secx)^2.tanx + sinx)/(6x) (0/0)
=(1/2)lim(x->0){ 2[(secx)^4+ 2(tanx)^2.(secx)^2] + cosx }/6
=[ 2(1+ 0) + 1 ]/12
=1/4