Question

For what value of k, the function given below is continuous at x = 0?

`f(x) = {{:((root  (4+x)-2)/x; x ≠ 0),(k  ; x = 0):}`

Options

• 0

• `1/4`

• 1

• 4

Answer 1

`1/4` 

Explanation: 

`f(x) = {{:((root  (4+x)-2)/x; x ≠ 0),(k  ; x = 0):}`

For continuity at x = 0

`lim_(x->0^+)[f(x)] = lim_(x->0^-)[f(x)] = f(0)`

`f(x) = (root  (4+x)-2)/x xx (root  (4+x)+2)/(root  (4+x)+2)`

`f(x) = (4+x-4)/(x(root  (4+x) +2))`

`f(x) = 1/(root  (4+x)+2)`

`= 1/(root  (4+x)+2)`

Let, x = 0+h

= `lim_(h->0) 1/root  (4+0+h+2) = 1/4`

Given f(0) = k

So, `[k = 1/4]`