Question

Assuming lim f(x)=4
x->6
lim x f(x)
x->4
Isn't that equal to 4 lim f(x)
x->4

Answer 1

Yes, we don't know anything about f(x) near 4.
\[lim_{x\rightarrow 6}{f(x)} = 4\]
\[lim_{x\rightarrow 4}{xf(x)} = 4lim_{x\rightarrow 4}{f(x)}\]