Question 19 - NCERT Exemplar - MCQs - Chapter 5 Class 12 Continuity and Differentiability (Term 1)
Last updated at Nov. 18, 2021 by Teachoo
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If
f
(x) = {(mx+1, if xβ€Ο/2 sinβ‘γx+n, if x> Ο/2γ)β€ , is continuous at x = Ο/2, then
Hello! Teachoo has made this answer with days (even weeks!) worth of effort and love. If Teachoo has been of any help to you in your Board exam preparation, then please support us by clicking on this link to make a donation
Question 19
If f (x) = {β(ππ₯+1, ππ π₯β€π/2@sinβ‘γπ₯+π, ππ π₯> π/2γ )β€ , is continuous at x = π/2, then
(A) m = 1, n = 0 (B) m = ππ/2 + 1
(C) n = ππ/2 (D) none of these
Given that function is continuous at π₯=π/2
Now,
π is continuous at π₯=π/2
If L.H.L = R.H.L = π(π/2)
i.e. limβ¬(xβγπ/2γ^β ) π(π₯)=limβ¬(xβγπ/2γ^+ ) " " π(π₯)= π(π/2)
LHL at x β π /π
(πππ)β¬(π₯βγπ/2γ^β ) f(x) = (πππ)β¬(ββ0) f ( π/2 β h)
= limβ¬(hβ0) m (Ο/2 β h) + 1
= m (π/2 β 0) + 1
= mπ /π+ 1
RHL at x β π /π
(πππ)β¬(π₯βγπ/2γ^+ ) f(x) = (πππ)β¬(ββ0) f ( π/2 + h)
= sin = limβ¬(hβ0) sin (Ο/2 + h) + n
(Ο/2 + 0) + n
= 1 + n
Since, f is continuous at π₯ =π/2
β΄ L.H.L = R.H.L
"m" π/2 "+ 1"="1 + n"
"m" π/2="n"
π§=ππ /π
So, the correct answer is (C)
Made by
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.
