Get live Maths 1-on-1 Classs - Class 6 to 12
Ex 5.1, 3 (b) - Chapter 5 Class 12 Continuity and Differentiability (Term 1)
Last updated at March 16, 2023 by Teachoo
Ex 5.1
Ex 5.1 ,1
Ex 5.1 ,2
Ex 5.1, 3 (a)
Ex 5.1, 3 (b) You are here
Ex 5.1, 3 (c) Important
Ex 5.1, 3 (d) Important
Ex 5.1 ,4
Ex 5.1 ,5 Important
Ex 5.1 ,6
Ex 5.1 ,7 Important
Ex 5.1 ,8
Ex 5.1, 9 Important
Ex 5.1, 10
Ex 5.1, 11
Ex 5.1, 12 Important
Ex 5.1, 13
Ex 5.1, 14
Ex 5.1, 15 Important
Ex 5.1, 16
Ex 5.1, 17 Important
Ex 5.1, 18 Important
Ex 5.1, 19 Important
Ex 5.1, 20
Ex 5.1, 21
Ex 5.1, 22 (i) Important
Ex 5.1, 22 (ii)
Ex 5.1, 22 (iii)
Ex 5.1, 22 (iv) Important
Ex 5.1, 23
Ex 5.1, 24 Important
Ex 5.1, 25
Ex 5.1, 26 Important
Ex 5.1, 27
Ex 5.1, 28 Important
Ex 5.1, 29
Ex 5.1, 30 Important
Ex 5.1, 31
Ex 5.1, 32
Ex 5.1, 33
Ex 5.1, 34 Important
Transcript
Ex 5.1, 3 Examine the following functions for continuity. (b) f (x) = 1/(𝑥 − 5) , x ≠ 5 f (x) = 1/(𝑥 − 5) At x = 5 f (x) = 1/(5 − 5) = 1/0 = ∞ Hence, f(x) is not defined at x = 5 So, we check for continuity at all points except 5 Let c be any real number except 5. f is continuous at 𝑥 = 𝑐 if (𝐥𝐢𝐦)┬(𝐱→𝒄) 𝒇(𝒙) = 𝒇(𝒄) LHS (𝐥𝐢𝐦)┬(𝐱→𝒄) 𝒇(𝒙) = lim┬(𝑥⟶𝑐)〖1/(𝑥 − 5)〗 = 1/(𝑐 − 5) RHS 𝒇(𝒄) = 1/(𝑐 − 5) Since, L.H.S = R.H.S ∴ Function is continuous at x = c (except 5) Thus, we can write that f is continuous for all real numbers except 5 ∴ f is continuous at each 𝐱 ∈ R − {𝟓}
