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
Examples
Example 1
Example 2
Example 3
Example 4 Important
Example 5
Example 6
Example 7
Example 8
Example 9
Example 10
Example 11
Example 12
Example 13
Example 14
Example 15
Example 16
Example 17 Important
Example 18 You are here
Example 19
Example 20 Important
Example 21
Example 22
Example 23
Example 24
Example 25
Example 26 Important
Example 27
Example 28
Example 29 Important
Example 30 Important
Example 31
Example 32 Important
Example 33 Important
Example 34
Example 35
Example 36 Important
Example 37 Important
Example 38
Example 39
Example 40
Example 41
Example 42 Important
Example 43
Example 44 Important
Example 45 Important
Example 46
Example 47 Important
Example 48
About the Author
Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.