Question

高数 求导数？

谢谢谢谢谢

Answer 1

第一题，=[x-sinx]/x^2/sinx=[x-sinx]/x^3，然后使用洛必达法则

Answer 2

(1)

x->0
sinx = x -(1/6)x^3+o(x^3)
x-sinx = (1/6)x^3+o(x^3)
lim(x->0) [ 1/(xsinx) -1/x^2]
=lim(x->0) (x-sinx)/(x^2.sinx)
=lim(x->0) (x-sinx)/x^3
=lim(x->0) (1/6)x^3/x^3
=1/6
(2)
x->0
a^x = 1+(lna)x +o(x)

b^x = 1+(lnb)x +o(x)
(a^x +b^x)/2 = 1+ (1/2)(ln(ab)).x +o(x)
lim(x->0) [(a^x +b^x)/2]^(1/x)
=lim(x->0) [ 1+ (1/2)(ln(ab)).x ]^(1/x)
=e^[(1/2)ln(ab)]
=√(ab)