Question

Determine the value of the constant 'k' so that function f(x) `{((kx)/|x|, ","if  x < 0),(3"," , if x >= 0):}` is continuous at x = 0

Answer 1

Given , f(x) = `{((kx)/|x|, ","if  x < 0),(3"," , if x >= 0):}` 

Since the function is continuous at x = 0 , therefore ,

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

⇒ `lim_(x → 0) (-kx)/x = lim_(x → 0)3 = 3`

⇒ -k = 3

⇒ k = -3