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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
Solution
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
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