Question

find k so that the following function is continuous on any interval:

h(x) = kcosx on 0 11 years ago

Answer 1

In order for h(x) to be continuous at \(x = 5\pi\),\[
\lim_{x \rightarrow 5\pi^-}h(x) = \lim_{x \rightarrow 5\pi^+}h(x) \\
\lim_{x \rightarrow 5\pi^-}k\cos(x) = \lim_{x \rightarrow 5\pi^+}(14-x) \\
k\cos(5\pi) = 14 - 5\pi \\
\cos(5\pi) = \cos(3\pi) = \cos(\pi) = -1 \\
-k = 14 - 5\pi \\ \\
k = 5\pi - 14
\]