Question

求极限，微积分问题，请看图

Answer 1

这两题是极限问题：

1. lim[(x+h)^3 - x^3]/h

   =lim[3x^2 * h + 3x * h^2 + h^3]/h

   =lim[3x^2 + 3x * h + h^2]

   =lim(3x^2) + lim(3x *h) + lim(h)^2

   =3x^2 + lim(3x * 0) + lim(0)^2

   =3x^2

2. =lim(1+u^3)^(1/4)/(1+u)

   =lim[(1+u^3)/(1+u)^4]^(1/4)

   =lim[(1+u)(1-u + u^2)/(1+u)^4]^(1/4)

   =lim[(1-u+u^2)/(1+u)^3]^(1/4)

   =lim[(1-u+u^2)/(1+3u+3u^2 + u^3)]^(1/4)

   =lim{[(1/u)^3 - (1/u)^2 + (1/u)]/[(1/u)^3 + 3*(1/u)^2 + 3*(1/u) + 1]}^(1/4)   注：分子、分母同除以 u^3

   =lim[(0^3 - 0^2 + 0)/(0^3 + 3*0^2 + 3*0 + 1)]^(1/4)

   =lim[0/1]^(1/4)

   =0

Answer 2