I've read the following claim, and wander how to prove or disprove it:
For a given function $f(z)=g(z)\cdot h(z)$ so that $\lim_{z\to0}g(z)=a$,
there is $h(z)$ so that $f(z)=g(z)\cdot [a+h(z)]$
and $\lim_{z\to0}h(z)=0$
Can someone explain that?
I've read the following claim, and wander how to prove or disprove it:
For a given function $f(z)=g(z)\cdot h(z)$ so that $\lim_{z\to0}g(z)=a$,
there is $h(z)$ so that $f(z)=g(z)\cdot [a+h(z)]$
and $\lim_{z\to0}h(z)=0$
Can someone explain that?
If I understand you correctly then this statement is false: $\lim_{z\to 0}g(z)=a$ $\lim_{z\to 0}h(z)=0$ Which means $\lim_{z\to 0}f(z)=\lim_{z\to 0}g(z)\lim_{z\to 0}h(z)=0\neq \lim_{z\to 0}f(z)=\lim_{z\to 0}g(z)\lim_{z\to 0}[a+h(z)]=a^2$