Question

Examine the continuity off at x = 1, if

f (x) = 5x - 3 , for 0 ≤ x ≤ 1

       = x² + 1 , for 1 ≤ x ≤ 2

Answer 1

`lim_(x -> 1)` f (x) = `lim_(x -> 1)` (5x - 3)

                            = 2

`lim_(x -> 1) = "f"("x") = lim_(x -> 1) ("x"^2 + 1)`

                                   = 2

f(1) = 1² + 1 = 2

As `lim_(x -> 1^-)` f(x)  = `lim_(x -> 1)` f(x) = f(1)

∴ f(x) is continuous at x = 1.