Example 12 - Chapter 5 Class 12 Continuity and Differentiability
Last updated at Dec. 16, 2024 by Teachoo
Last updated at Dec. 16, 2024 by Teachoo
Example 12 Discuss the continuity of the function defined by 𝑓(𝑥)={█(& 𝑥+2, 𝑖𝑓 𝑥<0@&−𝑥+2, 𝑖𝑓 𝑥>0)┤ 𝑓(𝑥)={█(& 𝑥+2, 𝑖𝑓 𝑥<0@&−𝑥+2, 𝑖𝑓 𝑥>0)┤ Here, function is not defined for x = 0 So, we do not check continuity there We check continuity for different values of x When x < 0 When x > 0Case 1 : When x < 0 For x < 0, f(x) = x + 2 Since this a polynomial It is continuous ∴ f(x) is continuous for x < 0 Case 2 : When x > 0 For x > 0, f(x) = −x + 2 Since this a polynomial It is continuous ∴ f(x) is continuous for x > 0 Hence, 𝑓 is continuous for all Real points except 0. Thus, 𝒇 is continuous for 𝒙 ∈𝐑−{𝟎}
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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 and Computer Science at Teachoo