Question

Find a value of k that makes f(x)= x^2,x is less than or equal to 1
and sin(kx), x > 1
continuous at x=1

Answer 1

at x=1, x^2 = 1
so, you need at x=1, sin(k) = 1
so where is sin(k) equal to 1?

Answer 2

I understand that, but Im not sure how to solve for the k ):

Answer 3

come on sin(π/2) = 1. So, k=π/2
so, f(x) = sin(π/2 x) for x>1
That way the limit on both left and right is f(x) = 1

Answer 4

Thank you.. I forgot about the unit circle