Question

If f(x) `= sqrt(4 + "x" - 2)/"x", "x" ne 0` be continuous at x = 0, then f(0) = ______.

Options

• `1/2`

• `1/4`

• 2

• `3/2`

Answer 1

If f(x) `= sqrt(4 + "x" - 2)/"x", "x" ne 0` be continuous at x = 0, then f(0) = `underlinebb(1/4)`.

Explanation:

f(0) = `lim_(x → 0) f(x)= lim_(x → 0) (sqrt(4 + x) − 2)/x`

= `lim_(x → 0)(sqrt(4 + x) − 2)/x xx (sqrt(4 + x) + 2)/(sqrt(4 + x) + 2)`

= `lim_(x → 0) (sqrt(4 + x) − 4)/(x (sqrt(4 + x) + 2)) = lim_(x → 0) x/(x(sqrt(4 + x) + 2))`

= `lim_(x → 0) 1/ (sqrt(4 + x) + 2)`

= `1/(2 + 2)`

= `1/4`