Question

In the following question, k=5.8

Let f(x)= {x sin (k/x) x ~= 0,
{L x = 0.

For the given value k, find the value of L so that f(x) is continuous at 0.

Many thanks!!

Answer 1

since |sin(k/x)| <= 1 for all x,
x*sin(k/x) -> 0 as x->0

so, L=0 will fill the hole at x=0.

Doesn't matter what k is.