Question

If f(x) = `{:{(tan^-1|x|; "when"  x ≠ 0), (pi/4;  "when"  x = 0):}`, then ______ 

Options

• `lim_{x→0^+}`f(x) x ≠ 0

• `lim_{x→0^-}`f(x) x ≠ 0

• f(x) is continuous at x = 0

• f(x) is not continuous at x = 0

Answer 1

If f(x) = `{:{(tan^-1|x|; "when"  x ≠ 0), (pi/4;  "when"  x = 0):}`, then f(x) is not continuous at x = 0.

Explanation:

 `lim_{x→0}f(x) = tan^-1(0) = 0 ≠ f(0)`

∴ f(x) is not continuous at x = 0.