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Question
Evaluate the following limit :
`lim_(theta -> 0) [(sin("m"theta))/(tan("n"theta))]`
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Solution
`lim_(theta -> 0) (sin("m"theta))/(tan("n"theta))`
= `lim_(theta -> 0) (((sin("m"theta))/theta))/(((tan("m"theta))/theta))` ...[∵ θ → 0, θ ≠ 0]
= `lim_(theta -> 0) ((sin("m"theta)/("m"theta)"h"))/((tan("n"theta)/("n"theta)))xx"m"/"n"`
= `"m"/"n" (lim_(theta -> 0) sin("m"theta)/("m"theta))/(lim_(theta -> 0) tan("n"theta)/("n"theta))`
= `"m"/"n"*1/1 ...[because theta -> 0"," therefore "m"theta"," "n"theta -> 0 "and" lim_(x -> theta) (sinx)/x = 1]`
= `"m"/"n"`
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