Algebra of continous functions

Chapter 5 Class 12 Continuity and Differentiability
Concept wise

### Transcript

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) = sinβ‘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