Question

Find k so that the function is continuous on any interval.

h(x) = k cos x 0 ≤ x ≤ 3π
h(x)= 10 − x 3π < x

I am confused on how to find k when it gives you 3pi? help please

Answer 1

#1: h(x) = k cos x 0 ≤ x ≤ 3π
#2: h(x)= 10 − x 3π < x

#2: limit as x->3π = 10-3π

#1: h(3π) = k cos3π = -k

So, you need
-k = 10-3π
k = 3π-10

#1: h(x) = (3π-10)cosx