
Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class
Ex 12.1
Ex 12.1, 2
Ex 12.1, 3
Ex 12.1, 4 Important
Ex 12.1, 5
Ex 12.1, 6 Important
Ex 12.1, 7
Ex 12.1, 8 Important
Ex 12.1, 9
Ex 12.1,10 Important
Ex 12.1, 11
Ex 12.1, 12
Ex 12.1, 13
Ex 12.1, 14 Important
Ex 12.1, 15 Important
Ex 12.1, 16
Ex 12.1, 17 Important
Ex 12.1, 18
Ex 12.1, 19 Important
Ex 12.1, 20
Ex 12.1, 21 Important
Ex 12.1, 22 Important
Ex 12.1, 23
Ex 12.1, 24
Ex 12.1, 25 Important
Ex 12.1, 26
Ex 12.1, 27
Ex 12.1, 28 Important
Ex 12.1, 29
Ex 12.1, 30 Important
Ex 12.1, 31 You are here
Ex 12.1, 32 Important
Last updated at May 29, 2023 by Teachoo
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