Question 4 - CBSE Class 12 Sample Paper for 2023 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards

Last updated at April 16, 2024 by Teachoo

The value of ‘k’ for which the function f(x)={(1 -cos⁡4x/8x ² ,if x≠0 k,if x=0 is continuous at x = 0 is

(a) 0 (b) -1 (c) 1 (d) 2

Transcript

Question 4 The value of ‘k’ for which the function 𝑓(𝑥)={█((1 −cos⁡4𝑥)/〖8𝑥〗^2 , 𝑖𝑓 𝑥≠0@&𝑘, 𝑖𝑓 𝑥=0)┤ is continuous at x = 0 is (a) 0 (b) -1 (c) 1 (d) 2At 𝒙=𝟎 f(x) is continuous at x = 0 if (𝐥𝐢𝐦)┬(𝐱→𝟎) 𝒇(𝒙) = 𝒇(𝟎) L.H.S (𝐥𝐢𝐦)┬(𝐱→𝟎) 𝒇(𝒙) "= " lim┬(x→0) (1 − 𝒄𝒐𝒔⁡𝟒𝒙)/〖8𝑥〗^2 Using cos 2θ = 1 − 2sin2 θ Putting θ = 2x "= " lim┬(x→0) (1 − (𝟏− 𝟐 〖𝐬𝐢𝐧〗^𝟐⁡𝟐𝒙 ))/〖8𝑥〗^2 "= " lim┬(x→0) (1 − 1 + 2 sin^2⁡2𝑥)/〖8𝑥〗^2 "= " lim┬(x→0) ( 2 sin^2⁡2𝑥)/〖8𝑥〗^2 "= " lim┬(x→0) ( sin^2⁡2𝑥)/〖4𝑥〗^2 "= " (𝐥𝐢𝐦)┬(𝐱→𝟎) (𝒔𝒊𝒏⁡𝟐𝒙/𝟐𝒙)^𝟐 = 1 R.H.S 𝒇(𝟎) = k Since f(x) is continuous at x = 0. 1 = k k = 1 So, the correct answer is (c)

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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.

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