Question

已知函数f(x)=√|x|*sin1/x^2,x不等于0;0,x=0.

Answer 1

x不为0时，f(x) = |x|^(1/2)sin(1/x^2),

lim_{x->0}f(x) = lim_{x->0}|x|^(1/2)sin(1/x^2) = 0 [sin(1/x^2)有界，|x|^(1/2)是无穷小量。。]

= f(0),

f(x)在x=0处连续。

lim_{x->0+}[f(x) - f(0)]/x = lim_{x->0+}...