Ex 13.1, 31 - If function f(x) lim x->1 f(x)-2/x2-1 = pi

Ex 13.1, 31 - Chapter 13 Class 11 Limits and Derivatives - Part 2

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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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.