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Question
Evaluate the following limit.
`lim_(x -> pi) (sin(pi - x))/(pi (pi - x))`
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Solution
`lim_(x → π)(sin(π - x))/(π (π - x))`
Let π − x = θ, When x → π, θ → 0
∴ `lim_(x → π) 1/π. (sin(π - x))/((π - x))`
= `lim_(θ → 0) (sinθ)/(πθ)`
= `lim_(θ → 0) 1/π. ((sin θ)/θ)`
= `1/π`
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