Question

Consider the function  `f(x) = x sin  pi/x`. What value must we give f(0) in order to make the function continuous everywhere?

Answer 1

 `f(x) = x sin  pi/x`

Define f(x) on R as

`f(x) = {{:(x sin  pi/x,  "if"  x ≠ 0),(0,  "if"  x = 0):}`

∴ f(0) = 0.

Then f(x) is continuous on R.