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Question
`lim_(x -> 0) |sinx|/x` is ______.
Options
1
–1
does not exist
None of these
Solution
`lim_(x -> 0) |sinx|/x` is does not exist.
Explanation:
Given `lim_(x -> 0) |sinx|/x`
L.H.L = `lim_(x -> 0^-) (-sinx)/x = - 1` ......`[because lim_(x -> 0) sinx/x = 1]`
R.H.L = `lim_(x -> 0^+) sinx/x` = 1
L.H.L ≠ R.H.L
So the limit does not exist.
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