Ex 5.1 ,5 - Chapter 5 Class 12 Continuity and Differentiability

Last updated at April 16, 2024 by

Ex 5.1 ,5 Is f(x) = {x x <=1, 5 x > 1 continuous at x = 0, 1, 2

Ex 5.1 ,5 - Chapter 5 Class 12 Continuity and Differentiability - Part 2
Ex 5.1 ,5 - Chapter 5 Class 12 Continuity and Differentiability - Part 3

Transcript

Ex 5.1, 5 Is the function f defined by 𝑓(𝑥)={█(𝑥, 𝑖𝑓 𝑥≤1@&5, 𝑖𝑓 𝑥>1)┤ continuous at 𝑥 = 0 ? At 𝑥 = 1 ? At 𝑥 = 2 ? Given 𝑓(𝑥)={█(𝑥, 𝑖𝑓 𝑥≤1@&5, 𝑖𝑓 𝑥>1)┤ At x = 0 For x = 0, f(x) = x Since this a polynomial It is continuous ∴ f(x) is continuous for x = 0 At x = 1 f(x) is continuous at 𝑥 =1 if L.H.L = R.H.L = 𝑓(1) if lim┬(x→1^− ) 𝑓(𝑥)=lim┬(x→1^+ ) " " 𝑓(𝑥)= 𝑓(1) 𝑓(𝑥)={█(𝑥, 𝑖𝑓 𝑥≤1@&5, 𝑖𝑓 𝑥>1)┤ Since there are two different functions on the left & right of 1, we take LHL & RHL . LHL at x → 1 lim┬(x→1^− ) f(x) = lim┬(h→0) f(1 − h) = lim┬(h→0) (1−ℎ) = 1 − 0 = 1 RHL at x → 1 lim┬(x→1^+ ) f(x) = lim┬(h→0) f(1 + h) = lim┬(h→0) 5 = 5 Since L.H.L ≠ R.H.L f(x) is not continuous at x = 1 At x = 2 For x = 2, f(x) = 5 Since this a constant function It is continuous ∴ f(x) is continuous for x = 2

Go Ad-free
Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

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.