Question

Given the function f(x)={sin2x, x≤π
3x-k, x>π
find the value of k that will make the function continuous.

Answer 1

For the function to be continuous at \(x=c\), you need to satisfy
\[\large\lim_{x\to c^-}f(x)=\lim_{x\to c^+}f(x)\]
and \(f(c)\) must exist and be equal to the value of the one-sided limits.