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Question
`lim_(x -> 0) (sin mx cot x/sqrt(3))` = 2, then m = ______.
Solution
`lim_(x -> 0) (sin mx cot x/sqrt(3))` = 2, then m = `(2sqrt(2))/3`.
Explanation:
Given `lim_(x -> 0) (sin mx cot x/sqrt(3))` = 2
= `lim_((x -> 0),(because mx -> 0)) (sin mx)/(mx) xx mx lim_(x -> 0) (cot x/sqrt(3))` = 2
= `1 xx mx xx lim_(x -> 0) 1/(tan /sqrt(3))` = 2
= `lim_(x -> 0) mx xx (x/sqrt(3))/(x/sqrt(3) * tan x/sqrt(3))` = 2
= `(mx)/(x/sqrt(3)) (1)` = 2
⇒ `sqrt(3)m` = 2
⇒ m = `2/sqrt(3) = (2sqrt(3))/3`
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