Show that the function f(x) = {((x^n - 1/x - 1), when x ≠ 1), (n, when x = 1) is continuous.

Question

Show that the function \(f(x) = \begin{cases} x^n - 1/x - 1, & \quad \text{when } x ≠ 1\text{}\\ n, & \quad \text{when } x = 1 \text{ } \end{cases}\) is continuous.

Answer 1

It is given that

\(f(x) = \begin{cases} x^n - 1/x - 1, & \quad \text{when } x ≠ 1\text{}\\ n, & \quad \text{when } x = 1 \text{ } \end{cases}\)

Consider left hand limit at x = 1

Therefore, f is continuous at x = n.