Question

How does one derive sinc(0)=1 from lim(sinx/x)=1? Would not sinc(0)->1 be a lot more accurate without explicitly defining that sinc(0)=1?

Answer 1

\[\lim_{x \rightarrow 0} \sin(x)/x = 1\]
However, the function \[\sin(x)/x\] is not defined in x = 0 (denominator cnanot be 0)

To make \[sinc(x)\] defined at any point, we say\[sinc(x)\] is 1.