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Example 18 - Prove that f(x) = tan x is a continuous function

Example 18 - Chapter 5 Class 12 Continuity and Differentiability - Part 2


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Example 18 Prove that the function defined by f (x) = tan x is a continuous function.Let 𝑓(π‘₯) = tan⁑π‘₯ 𝒇(𝒙) = 𝐬𝐒𝐧⁑𝒙/πœπ¨π¬β‘π’™ Here, 𝑓(π‘₯) is defined for all real number except 𝒄𝒐𝒔⁑𝒙 = 0 i.e. for all x except x = (πŸπ’+𝟏) 𝝅/𝟐 Let 𝑝(π‘₯)=sin⁑π‘₯ & π‘ž(π‘₯)=cos⁑π‘₯ We know that sin x & cos⁑π‘₯ is continuous for all real numbers. Therefore, 𝑝(π‘₯) & π‘ž(π‘₯) is continuous. By Algebra of continuous function If 𝑝, π‘ž are continuous , then 𝒑/𝒒 is continuous. Thus, Rational Function 𝑓(π‘₯) = sin⁑π‘₯/cos⁑π‘₯ is continuous for all real numbers except at points where π‘π‘œπ‘  π‘₯ = 0 i.e. π‘₯ β‰ (2𝑛+1) πœ‹/2 Hence, tan⁑π‘₯ is continuous at all real numbers except 𝒙=(πŸπ’+𝟏) 𝝅/𝟐

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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.