Chapter 5 Class 12 Continuity and Differentiability
Ex 5.1, 13
Ex 5.1, 16
Ex 5.1, 18 Important
Ex 5.1, 28 Important
Ex 5.1, 30 Important
Ex 5.1, 34 Important
Ex 5.2, 5
Ex 5.2, 9 Important You are here
Ex 5.2, 10 Important
Ex 5.3, 10 Important
Ex 5.3, 14
Example 29 Important
Example 30 Important
Ex 5.5,6 Important
Ex 5.5, 7 Important
Ex 5.5, 11 Important
Ex 5.5, 16 Important
Ex 5.6, 7 Important
Ex 5.6, 11 Important
Example 38 Important
Ex 5.7, 14 Important
Question 4 Important Deleted for CBSE Board 2025 Exams
Question 5 Important Deleted for CBSE Board 2025 Exams
Example 39 (i)
Example 40 (i)
Example 42 Important
Misc 6 Important
Misc 15 Important
Misc 16 Important
Misc 22 Important
Chapter 5 Class 12 Continuity and Differentiability
Last updated at April 16, 2024 by Teachoo
Ex 5.2, 9 Prove that the function f given by ๐ (๐ฅ) = | ๐ฅ โ 1|, ๐ฅ โ ๐ is not differentiable at x = 1. f(x) = |๐ฅโ1| = {โ((๐ฅโ1), ๐ฅโ1โฅ0@โ(๐ฅโ1), ๐ฅโ1<0)โค = {โ((๐ฅโ1), ๐ฅโฅ1@โ(๐ฅโ1), ๐ฅ<1)โค Now, f(x) is a differentiable at x = 1 if LHD = RHD (๐๐๐)โฌ(๐กโ๐) (๐(๐) โ ๐(๐ โ ๐))/๐ = (๐๐๐)โฌ(hโ0) (๐(1) โ ๐(1 โ โ))/โ = (๐๐๐)โฌ(hโ0) (|1 โ 1|โ|(1 โ โ)โ1|)/โ = (๐ ๐๐)โฌ(hโ0) (0 โ|โโ|)/โ = (๐๐๐)โฌ(hโ0) (0 โ โ)/โ = (๐๐๐)โฌ(hโ0) (โโ)/โ = (๐๐๐)โฌ(hโ0) (โ1) = โ1 (๐๐๐)โฌ(๐กโ๐) (๐(๐ + ๐) โ ๐(๐))/๐ = (๐๐๐)โฌ(hโ0) (๐(1 + โ) โ ๐(1))/โ = (๐๐๐)โฌ(hโ0) (|(1 + โ) โ 1|โ|1 โ 1|)/โ = (๐๐๐)โฌ(hโ0) (|โ| โ 0)/โ = (๐๐๐)โฌ(hโ0) (โ โ 0)/โ = (๐๐๐)โฌ(hโ0) โ/โ = (๐๐๐)โฌ(hโ0) (1) = 1 Since LHD โ RHD โด f(x) is not differentiable at x = 1 Hence proved