Let $f(x, y) = \begin{cases} \frac{sin(x^2+y^2-1)}{x^2+y^2-1} & x^2 + y^2 \neq 1 \\ b & x^2 + y^2 = 1 \end{cases} $. Find the value of b for which f is continuous at all the point on $\mathbb R^2$
Attempt:
Since
$\lim_{x^2+y^2 \to 1} f(x, y) = \lim_{x^2+y^2 - 1 \to 0} \frac{sin(x^2+y^2-1)}{x^2+y^2-1} = 1$
To make f continuous at all points in $\mathbb R^2$, then it needs to be 1?
Would this be right?