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Question
`lim_(x -> 0) (tan 2x - x)/(3x - sin x)` is equal to ______.
Options
2
`1/2`
`-1/2`
`1/4`
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Solution
`lim_(x -> 0) (tan 2x - x)/(3x - sin x)` is equal to `1/2`.
Explanation:
Given `lim_(x -> 0) (tan 2x - x)/(3x - sin x)`
= `lim_(x -> 0) (x[tan2x/x - 1])/(x[3 - sin x/x])`
`lim_((x -> 0),(because 2x -> 0)) ((tan 2x)/(2x) xx 2 - 1)/(3 - sinx/x)`
= `(1.2 - 1)/(3 - 1)`
= `(2 - 1)/2`
= `1/2`
∴ 2x → 0
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