Check sibling questions

The function f (x) = {8(sin⁑x/x " + cos x, if x " β‰ " 0" k", if x " =" 0" )─ is continuous at x = 0, then the value of k is

(A) 3Β  Β Β Β 

(B) 2

(C) 1Β  Β  Β 

(D) 1.5

Β 

This question is similar to Ex 5.1, 18 - Chapter 5 Class 12 - Continuity and Differentiability

Slide1.JPG

Slide2.JPG
Slide3.JPG

Get Real time Doubt solving from 8pm to 12 am!


Transcript

Question 1 The function f (x) = {β– 8(sin⁑π‘₯/π‘₯ " + cos x, if x " β‰ " 0" @π‘˜ ", if x " =" 0" )─ is continuous at x = 0, then the value of k is (A) 3 (B) 2 (C) 1 (D) 1.5 At 𝒙 = 0 f(x) is continuous at π‘₯=0 if L.H.L = R.H.L = 𝑓(0) if if lim┬(xβ†’0^βˆ’ ) 𝑓(π‘₯) = lim┬(xβ†’0^+ ) 𝑓(π‘₯) = 𝑓(0) LHL at x β†’ 0 (π’π’Šπ’Ž)┬(π±β†’πŸŽ^βˆ’ ) f(x) = lim┬(hβ†’0) f(0 βˆ’ h) = (π’π’Šπ’Ž)┬(π‘β†’πŸŽ) f(βˆ’h) = lim┬(hβ†’0) sin⁑〖(βˆ’β„Ž)γ€—/((βˆ’β„Ž)) " + cos (βˆ’ h)" = (π’π’Šπ’Ž)┬(π‘β†’πŸŽ) γ€–βˆ’π’”π’Šπ’γ€—β‘π’‰/(βˆ’π’‰) " +" (π’π’Šπ’Ž)┬(π‘β†’πŸŽ) " cos h" = lim┬(hβ†’0) sinβ‘β„Ž/β„Ž " + " (π‘™π‘–π‘š)┬(β„Žβ†’0) " cos h" Using lim┬(xβ†’0) sin⁑π‘₯/π‘₯=1 = 1 + "cos 0" = 1 + 1 = 2 RHL at x β†’ 0 (π’π’Šπ’Ž)┬(π’™β†’πŸŽ^+ ) f(x) = lim┬(hβ†’0) f(0 + h) = (π’π’Šπ’Ž)┬(π‘β†’πŸŽ) f(h) = lim┬(hβ†’0) sinβ‘β„Ž/β„Ž " + cos h" = (π’π’Šπ’Ž)┬(π‘β†’πŸŽ) π’”π’Šπ’β‘π’‰/𝒉 " + " (π’π’Šπ’Ž)┬(π‘β†’πŸŽ) " cos h" Using lim┬(xβ†’0) sin⁑π‘₯/π‘₯=1 = 1 + "cos 0" = 1 + 1 = 2 At 𝒙=𝟎 𝑓(π‘₯)=π‘˜ 𝒇(𝟎)=π’Œ Since f(x) is continuous at x = 0. L.H.L = R.H.L = 𝑓(0) 𝑓(0)=2 π’Œ=𝟐 So, the correct answer is (B)

Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.