The value of ‘k’ for which the function f(x)={(1 -cos4x/8x ^{ 2 } ,if x≠0 k,if x=0 is continuous at x = 0 is
(a) 0 (b) -1 (c) 1 (d) 2
CBSE Class 12 Sample Paper for 2023 Boards
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CBSE Class 12 Sample Paper for 2023 Boards
Last updated at April 16, 2024 by Teachoo
Question 4 The value of βkβ for which the function π(π₯)={β((1 βcosβ‘4π₯)/γ8π₯γ^2 , ππ π₯β 0@&π, ππ π₯=0)β€ is continuous at x = 0 is (a) 0 (b) -1 (c) 1 (d) 2At π=π f(x) is continuous at x = 0 if (π₯π’π¦)β¬(π±βπ) π(π) = π(π) L.H.S (π₯π’π¦)β¬(π±βπ) π(π) "= " limβ¬(xβ0) (1 β πππβ‘ππ)/γ8π₯γ^2 Using cos 2ΞΈ = 1 β 2sin2 ΞΈ Putting ΞΈ = 2x "= " limβ¬(xβ0) (1 β (πβ π γπ¬π’π§γ^πβ‘ππ ))/γ8π₯γ^2 "= " limβ¬(xβ0) (1 β 1 + 2 sin^2β‘2π₯)/γ8π₯γ^2 "= " limβ¬(xβ0) ( 2 sin^2β‘2π₯)/γ8π₯γ^2 "= " limβ¬(xβ0) ( sin^2β‘2π₯)/γ4π₯γ^2 "= " (π₯π’π¦)β¬(π±βπ) (πππβ‘ππ/ππ)^π = 1 R.H.S π(π) = k Since f(x) is continuous at x = 0. 1 = k k = 1 So, the correct answer is (c)