Question

The value of f(0) for the function `f(x) = 1/x[log(1 + x) - log(1 - x)]` to be continuous at x = 0 should be

Options

• – 1

• 0

• – 2

• 2

Answer 1

2

Explanation:

Given `f(x) = 1/x[log(1 + x) - log(1 - x)]`

`lim_(x -> 0) f(x) = lim_(x -> 0)[(log(1 + x))/x + log[1 + (-x)]/((-x))]` = 1 + 1 = 2

Since `f(x)` is continuous at x = 0

∴ `lim_(x -> 0) f(x) = f(0)` = 2.