Ex 12.1, 31 - Chapter 12 Class 11 Limits and Derivatives

Last updated at May 7, 2024 by

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Ex 12.1, 31 If the function f(x) satisfies lim┬(x → 1) (𝑓(𝑥) − 2)/(𝑥2 − 1) = π , evaluate lim┬(x→1) f(x) . Given 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) (x2 – 1) lim┬(x→1) f(x) – lim┬(x→1) 2 = π (lim┬(x→1) x2 – lim┬(x→1) 1) By Algebra of limits (𝑙𝑖𝑚)┬(𝑥→𝑎) (𝑓(𝑥))/(𝑔(𝑥)) = ((𝑙𝑖𝑚)┬(𝑥→𝑎) 𝑓(𝑥))/((𝑙𝑖𝑚)┬(𝑥→𝑎) 𝑔(𝑥)) (lim┬(x→1) 𝑓(𝑥) − 2)/(lim┬(x→1) 〖(𝑥〗^2 − 1) ) = π lim┬(x→1) (f(x) – 2) = π × lim┬(x→1) (x2 – 1) lim┬(x→1) f(x) – lim┬(x→1) 2 = π (lim┬(x→1) x2 – lim┬(x→1) 1) Finding limits, putting x = 1 lim┬(x→1) f(x) – 2 = π × ((1)2 – 1) lim┬(x→1) f(x) – 2 = π × 0 lim┬(x→1) f(x) – 2 = π × 0 lim┬(x→1) f(x) – 2 = 0 lim┬(x→1) f(x) = 2 Thus (𝒍𝒊𝒎)┬(𝐱→𝟏) f (x) = 2

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.