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Question
`lim_("x" -> 0) (1 - "cos" 4 "x")/"x"^2` is equal to ____________.
Options
0
8
None of these
`1/2`
MCQ
Fill in the Blanks
Solution
`lim_("x" -> 0) (1 - "cos" 4 "x")/"x"^2` is equal to 8.
Explanation:
`= lim_("x" -> 0) (1 - "cos" 4 "x")/"x"^2`
`= lim_("x" -> 0) (4 "sin" 4 "x")/(2 "x")`
`= lim_("x" -> 0) (16 "cos" 4 "x")/2 = 8` (using L’Hospital Rule)
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