Question

求极限当X趋近与0时cos(sinx)-cosx/x^4

Answer 1

根据同阶无穷小，x→0时，sinx～x
lim(x→0)cos(sinx)-cosx/x^4
=lim(x→0)cosx-cosx/x^4
=lim(x→0)cosx(1-1/x^4)
=lim(x→0)cosx*lim(x→0)(1-1/x^4)
=1*lim(x→0)(1-1/x^4)
=-∞

Answer 2

=(-2 ( (sin(sinx+x)/2)*(sin(sinx-x)/2))/x^4
=(-2( (sinx+x)/2)*(sinx-x)/2))/x^4
=(-2( (sinx+x)/2)/x*(sinx-x)/2)/x^3)
=1/6