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NCERT Class XI Mathematics - Limits and Derivatives - Solutions

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Question : 31
Total: 72
If the function f(x) satisfies
lim
x→1
f(x)−2
x2−1
 = π, evaluate
lim
x→1
 f (x).
Solution:  
We have
lim
x→1
f(x)−2
x2−1
 = π
Since
lim
x→1
 (x2−1) = 0
∴ For
lim
x→1
f(x)−2
x2−1
 to exist, we must have
lim
x→1
 [f (x) - 2] = 0
[Since
lim
x→1
 (f (x) - 2) ≠ 0, then the given limit can’t exist]
⇒
lim
x→1
 f (x) - 2 = 0 ⇒ $\lim↙{x→1} f (x) = 2.
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