Question

有关高数求极限的题目

x->0时，求(1/x)[(1/x)-cotx)]的值

Answer 1

lim (1-xcotc)/x^2
=lim(tanx-x)/(x^2*tanx)
=lim(tanx-x)/x^3
=lim(sec^2x-1)/3x^2
=lim2sec^2xtanx/6x
=lim xsec^2x/3x
=1/3

Answer 2

lim1/x^2-xcotx/x^2=(1-xcotx)/x^2=(1-x/tanx)/x^2=(tanx-x)/(x^2tanx)=(tanx-x)/x^3=(sec^2x-1)/3x^2=tanx/(3x^2)=1/3