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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
Solution
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.
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