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Question
`lim_("x"->0) (1 - "cos x")/"x"` is equal to ____________.
Options
None of these
0
1
`1/2`
MCQ
Fill in the Blanks
Solution
`lim_("x"->0) (1 - "cos x")/"x"` is equal to 0.
Explanation:
`= lim_ ("x" -> 0) (1 - "cos x")/"x"`
`= lim_("x" -> 0) ((1 - "cos x")(1 + "cos x"))/("x" (1 + "cos x"))`
`= lim_("x" -> 0) "sin x"/"x". "sin x"/((1 + "cos x")) = 0`
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