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Question
If the function f(x) satisfies `lim_(x -> 1) (f(x) - 2)/(x^2 - 1) = pi`, evaluate `lim_(x -> 1) f(x)`.
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Solution
`lim_(x → 1) (f(x) - 2)/(x^2 - 1)` = π
⇒ `(lim_(x → 1) (f(x) - 2))/(lim_(x → 1)(x^2 - 1)` = π
⇒ `lim_(x → 1) (f(x) - 2) = π lim_(x → 1)(x^2 - 1)`
⇒ `lim_(x → 1) (f(x) - 2) = π (1^2 - 1)`
⇒ `lim_(x → 1) (f(x) - 2) = 0`
⇒ `lim_(x → 1) f(x) - lim_(x → 1) 2 = 0`
⇒ `lim_(x → 1) f(x) - 2 = 0`
∴ `lim_(x → 1) f(x) = 2`
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