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Question
`lim_(x -> 0) sinx/(x(1 + cos x))` is equal to ______.
Options
0
`1/2`
1
–1
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Solution
`lim_(x -> 0) sinx/(x(1 + cos x))` is equal to `1/2`.
Explanation:
We have `lim_(x -> 0) sinx/(x(1 + cos x))`
= `lim_(x -> 0) (2sin x/2 cos x/2)/(x 2 cos^2 x/2)`
= `1/2 lim_(x -> 0) (tan x/2)/(x/2)`
= `1/2`
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