Question

高数：一道极限题 cos(sinx)

Answer 1

lim[cos(sinx)-cosx]/x^4

cosx=1-(1/2)x^2+(1/24)x^4+o(x^4)

sinx=x-(1/6)x^3+o(x^3)

cos(sinx)=1-(1/2)(x-(1/6)x^3)^2+(1/24)x^4+o(x^4)

=1-(1/2)x^2+(1/6)x^4+(1/24)x^4+o(x^4)

原式=lim[1-(1/2)x^2+(1/6)x^4+(1/24)x^4-(1-(1/2)x^2+(1/24)x^4)+o(x^4)]/x^4

=1/6