1）lim cos(x/2)cos(x/2^2)...cos(x/2^n)
= lim sin(x/2^n)*[cos(x/2)cos(x/2^2)...cos(x/2^n)]/sin(x/2^n)
= lim [sinx/(2^n)*]/sin(x/2^n)
= (sinx/x)*lim [x/(2^n)]/sin(x/2^n)
= sinx/...
几道高数关于极限方面的问题III
1）lim cos(x/2)cos(x/2^2)...cos(x/2^n)
= lim sin(x/2^n)*[cos(x/2)cos(x/2^2)...cos(x/2^n)]/sin(x/2^n)
= lim [sinx/(2^n)*]/sin(x/2^n)
= (sinx/x)*lim [x/(2^n)]/sin(x/2^n)
= sinx/...