Question

If f(x) = `(sin(x^2 - x))/x`, x ≠ 0, is continuous at x = 0, then f(0) is ______ 

Options

• -1

• 0

• 1

• 2

Answer 1

If f(x) = `(sin(x^2 - x))/x`, x ≠ 0, is continuous at x = 0, then f(0) is -1. 

Explanation:

Since, f(x) is continuous at x = 0.

∴ f(0) = `lim_{x→0} f(x) = lim_{x→0} (sin(x^2 - x))/x`

= `lim_{x→0} (sin[x(x - 1)])/(x(x - 1)) xx (x - 1)`

= `1 xx (-1) = -1`