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NCERT Class XI Mathematics - Limits and Derivatives - Solutions

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Question : 31 of 72
Marks: +1, -0
If the function f(x) satisfies limx1f(x)2x21\lim\limits_{x\to 1}\frac{f(x)-2}{x^2-1} = π, evaluate limx1\lim\limits_{x\to 1} f (x).
Solution:  
We have limx1f(x)2x21\lim\limits_{x\to 1}\frac{f(x)-2}{x^2-1} = π
Since limx1\lim\limits_{x\to 1} (x21)(x^2-1) = 0
∴ For limx1\lim\limits_{x\to 1} f(x)2x21\frac{f(x)-2}{x^2-1} to exist, we must have limx1\lim\limits_{x\to 1} [f (x) - 2] = 0
[Since limx1\lim\limits_{x\to 1} (f (x) - 2) ≠ 0, then the given limit can’t exist]
limx1\lim\limits_{x\to 1} f (x) - 2 = 0 ⇒ $\lim↙{x→1} f (x) = 2.
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