Question

If f(x) = `{{:((kx)/|x|"," if x < 0),(  3","   if x ≥ 0):}` is continuous at x = 0, then the value of k is ______.

Options

• –3

• 0

• 3

• any real number

Answer 1

If f(x) = `{{:((kx)/|x|"," if x < 0),(  3","   if x ≥ 0):}` is continuous at x = 0, then the value of k is –3.

Explanation:

Since, f is continuous at x = 0,

Therefore, L.H.L = R.H.L = f(0) = a finite quantity.

`lim_(x rightarrow 0^-) f(x) = lim_(x rightarrow 0^+) f(x)` = f(0)

`\implies lim_(x rightarrow 0^-) (-kx)/x = lim_(x rightarrow0^+)3` = 3

`\implies` k = –3.