Question

考研高等数学 泰勒公式的应用lim(x趋近于0)(tan(tanx)-sin(sinx))/(x-sinx)

Answer 1

lim(x趋近于0)(tan(tanx)-sin(sinx))/(x-sinx)

=lim(x趋近于0)[(x+x^3/3+(x+x^3/3)^3/3)+o(x^3)]-[x-x^3/6-(x-x^3/6)^3+o(x^3)]/[x-(x-x^3/6+o(x^3)]=[(2/3)+(1/3)]/(1/6)=6