Ex 5.1

Chapter 5 Class 12 Continuity and Differentiability
Serial order 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

Made by

#### Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.