In the worked example of Differentiation: Part A: Session 8, It's written that:
"Because lim (as x tends to zero) of sin (x) / x = 1, we know that sinc(0) = 1."
How is sinc(0) = 1 ?? I know that limit = 1 but the function stills undefined at x = 0, right ??

The second question is:
In the second page of the same example, they said:
"as x

Question

In the worked example of Differentiation: Part A: Session 8, It's written that:
"Because lim (as x tends to zero) of sin (x) / x = 1, we know that sinc(0) = 1."
How is sinc(0) = 1 ?? I know that limit = 1 but the function stills undefined at x = 0, right ??

The second question is:
In the second page of the same example, they said:
"as x < 0, sin (x) is negative"
But isn't sin (x) oscillating between Positive and Negative, (i.e sin (-270 degrees) = 1)

phi · Answer

Perhaps they should say that the sinc(0) has *by definition*, the value $$ \lim_{x\rightarrow 0} \frac{\sin(x)}{x} = 1$$ and yes, you do get an oscillation. a plot of sinc(x) looks like this http://mathworld.wolfram.com/SincFunction.html

anonymous · Answer

But why is the function sinc(x) defined at x = 0 ?? (The graph of the function is not placing a little open circle at the point (0, 1))