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Question
`lim_(x→0) sqrt(1 - cosx)/(sqrt(2)x)` is ______.
Options
1
–1
zero
does not exist
MCQ
Fill in the Blanks
Solution
`lim_(x→0) sqrt(1 - cosx)/(sqrt(2)x)` is does not exist.
Explanation:
`lim_(x→0) sqrt(1 - cosx)/(sqrt(2)x)`;
`lim_(x→0) sqrt(2sin^2x)/(sqrt(2)x)`
⇒ `lim_(x→0) |sinx|/x` ...`[∵ lim_(x→0) sinθ/θ = 1]`
The limit of above does not exist as
LHS = –1 ≠ RHL = 1
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