1. Chapter 5 Class 12 Continuity and Differentiability
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Ex 5.1, 21 Discuss the continuity of the following functions: (a) π (π₯) = sinβ‘π₯+cosβ‘π₯ π (π₯) = sinβ‘π₯+cosβ‘π₯ Let π(π₯)=sinβ‘π₯ & π(π₯)=cosβ‘π₯" " We know that sinβ‘π₯ & cosβ‘π₯ both continuous function β π(π₯) & π(π₯) is continuous at all real number By Algebra of continuous function If π(π₯)" & " π(π₯) are continuous for all real numbers then π(π₯)= π(π₯)+π(π₯) is continuous for all real numbers β΄ π(π) = π¬π’π§β‘π+πππβ‘π continuous for all real numbers Ex 5.1, 21 Discuss the continuity of the following functions: (b) π (π₯) = sinβ‘π₯ β cosβ‘π₯ π (π₯) = sinβ‘π₯ β cosβ‘π₯ Let π(π₯)=sinβ‘π₯ & π(π₯)=cosβ‘π₯" " We know that sinβ‘π₯ & cosβ‘π₯ are both continuous function β π(π₯) & π(π₯) is continuous at all real number By Algebra of continuous function If π(π₯)" & " π(π₯) are continuous for all real numbers then π(π₯)= π(π₯)βπ(π₯) is continuous for all real numbers β΄ π(π) = πππβ‘πβπππβ‘π is continuous for all real numbers Ex 5.1, 21 Discuss the continuity of the following functions: (c) π (π₯) = sinβ‘π₯ . cosβ‘π₯ π (π₯) = sinβ‘π₯ . cosβ‘π₯ Let π(π₯)=sinβ‘π₯ & π(π₯)=cosβ‘π₯" " We know that sinβ‘π₯ & cosβ‘π₯ are both continuous functions β π(π₯) & π(π₯) is continuous at all real numbers By Algebra of continuous function If π(π₯)" & " π(π₯) are continuous for all real numbers then π(π₯)= π(π₯) . π(π₯) is continuous for all real numbers β΄ π(π) = πππβ‘π.πππβ‘π continuous for all real numbers

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