Question

求同阶无穷小n→0时exp(tan(x))-exp(sin(x))为x的n阶无穷小,求n用过泰勒公式了，能算出来，但太烦

Answer 1

exp(tan(x))-exp(sin(x))

=exp(sinx)[exp(tan(x)-sin(x))-1],(x->0)

=exp(tan(x)-sin(x))-1,(exp(x)-1 ~ x,x->0)

=tan(x)-sin(x)

=[sinx(1-cosx)]/cosx,(x->0)

=sinx(1-cosx)

所以n=3