Question

若要函数f(x)在x=2处连续,则应定义f(x)=_____.我用几何画板画出来不造是1/3还是1诶~

Answer 1

f(x) 分子分母同乘以 [4+2(6+x)^(1/3)+(6+x)^(2/3)][2+√(2+x)],

则 lim[2-(6+x)^(1/3)]/[2-√(2+x)]

= lim(2-x)[2+√(2+x)]/{(2-x)[4+2(6+x)^(1/3)+(6+x)^(2/3)]}

= lim[2+√(2+x)]/[4+2(6+x)^(1/3)+(6+x)^(2/3)]

= 4/(4+4+4) = 1/3.

则应定义 f(2) = 1/3 .