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 August 12, 2026 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

$[MCQ] The value of ‘k’ for which function f(x) = { 1 - cos4x / 8x^2 - CBSE Class 12 Sample Paper for 2023 Boards$

part 2 - Question 4 - CBSE Class 12 Sample Paper for 2023 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards - Class 12

part 3 - Question 4 - CBSE Class 12 Sample Paper for 2023 Boards - Solutions of Sample Papers and Past Year Papers - for Class 12 Boards - Class 12

Next: Question 5 → Remove Ads

Teachoo · Class 12 Explore Class 12

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)

Made by

Davneet Singh

Davneet Singh is an IIT Kanpur graduate and has been teaching for 16+ years. At Teachoo, he breaks down Maths, Science and Computer Science into simple steps so students understand concepts deeply and score with confidence.

Many students prefer Teachoo Black for a smooth, ad-free learning experience.

Class 6

Class 7

Class 8

Class 9

Class 10

Class 11

Class 12

Courses

Interesting

Popular