Ex 5.1, 22 (iv) - Chapter 5 Class 12 Continuity and Differentiability

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Prove that cotangent function is continous [with Video] - Teachoo

Ex 5.1, 22 (iv) - Chapter 5 Class 12 Continuity and Differentiability - Part 2

Transcript

Ex 5.1, 22 (iv) Discuss the continuity of cotangent functions.Let 𝒇(𝒙) = 𝒄𝒐𝒕 𝒙 𝑓(π‘₯) = cos⁑π‘₯/sin⁑π‘₯ 𝑓(π‘₯) is defined for all real number except where sin⁑π‘₯ = 0 i.e. x = 𝒏𝝅 Let 𝒑(𝒙)=cos⁑π‘₯ & 𝒒(𝒙)=sin⁑π‘₯ We know that sin⁑π‘₯ & cos x is continuous for all real number ∴ p(x) & q (x) are continuous functions By Algebra of continuous function If 𝑝, π‘ž are continuous , then 𝒑/𝒒 is continuous. Thus, 𝑓(π‘₯) = cos⁑π‘₯/sin⁑π‘₯ is continuous for all real numbers except where sin⁑π‘₯ = 0 i.e. 𝒙= 𝒏𝝅, π’βˆˆπ’ So, 𝒄𝒐𝒕 𝒙 is continuous at all real numbers except where 𝒙= 𝒏𝝅, π’βˆˆπ’

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