Ex 5.1, 22 (iv) - Chapter 5 Class 12 Continuity and Differentiability
Last updated at Dec. 16, 2024 by Teachoo
Last updated at Dec. 16, 2024 by Teachoo
Ex 5.1, 22 (iv) Discuss the continuity of cotangent functions.Let π(π) = πππ π π(π₯) = cosβ‘π₯/sinβ‘π₯ π(π₯) is defined for all real number except where sinβ‘π₯ = 0 i.e. x = ππ Let π(π)=cosβ‘π₯ & π(π)=sinβ‘π₯ We know that sinβ‘π₯ & cos x is continuous for all real number β΄ p(x) & q (x) are continuous functions By Algebra of continuous function If π, π are continuous , then π/π is continuous. Thus, π(π₯) = cosβ‘π₯/sinβ‘π₯ is continuous for all real numbers except where sinβ‘π₯ = 0 i.e. π= ππ , πβπ So, πππ π is continuous at all real numbers except where π= ππ , πβπ
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