Example 18 - Chapter 5 Class 12 Continuity and Differentiability
Last updated at Dec. 8, 2016 by Teachoo
Transcript
Example 18 Prove that the function defined by f (x) = tan x is a continuous function. Let 𝑓𝑥 = tan𝑥 𝑓𝑥 = sin𝑥cos𝑥 is defined for all real number except cos𝑥 = 0 i.e. x = 2𝑛+1 𝜋2 Let 𝑝𝑥=sin𝑥 & 𝑞𝑥=cos𝑥 We know that sin x & cos𝑥 is continuous for all real numbers. ⇒ 𝑝𝑥 & 𝑞𝑥 is continuous. By Algebra of continuous function If 𝑝𝑥 & 𝑞𝑥 both continuous for all real numbers then 𝑓𝑥= 𝑝𝑥𝑞𝑥 , is continuous for all real numbers such that 𝑞𝑥 ≠ 0 ⇒ 𝑓𝑥 = sin𝑥cos𝑥 is continuous for all real numbers such that cos𝑥 ≠ 0 i.e. 𝑥 ≠2𝑛+1𝜋2 Hence, tan𝑥 is continuous at all real numbers except 𝒙=𝟐𝒏+𝟏𝝅𝟐
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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.