当x趋近于0时,求[∫(0,x) t/(1+t)^(1/2)dt] / (tanx)^2的极限
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/17 22:09:57
![当x趋近于0时,求[∫(0,x) t/(1+t)^(1/2)dt] / (tanx)^2的极限](/uploads/image/z/14309348-68-8.jpg?t=%E5%BD%93x%E8%B6%8B%E8%BF%91%E4%BA%8E0%E6%97%B6%2C%E6%B1%82%5B%E2%88%AB%280%2Cx%29+t%2F%281%2Bt%29%5E%281%2F2%29dt%5D+%2F+%28tanx%29%5E2%E7%9A%84%E6%9E%81%E9%99%90)
x){wrŋm/O|m:66E?XaSPa]aoRQWg|V˳y/gNI*ҧ9v6sQNfQڐeot^7Xճ;Q/.,Iyyӎ`)[} k*h,1YH/3DVDօ-$H,_W 5 (͜';z7=[F 1 B
当x趋近于0时,求[∫(0,x) t/(1+t)^(1/2)dt] / (tanx)^2的极限
当x趋近于0时,求[∫(0,x) t/(1+t)^(1/2)dt] / (tanx)^2的极限
当x趋近于0时,求[∫(0,x) t/(1+t)^(1/2)dt] / (tanx)^2的极限
lim [∫(0,x) t/(1+t)^(1/2)dt] / (tanx)^2
当x趋于0时,该极限为0/0型
根据L'Hospital法则
=lim (x/(1+x)^(1/2)) / (2*tanx*(1/cos^2x))
=lim (x*cos^2x) / (2*(1+x)^(1/2)*tanx)
=lim cos^2x / (2(1+x)^(1/2)) *lim x / tanx
=(1/2)*lim x/sinx * lim cosx
=1/2
有不懂欢迎追问