Example 19 - Chapter 5 Class 12 Continuity and Differentiability
Last updated at Dec. 16, 2024 by Teachoo
Last updated at Dec. 16, 2024 by Teachoo
Example 19 Show that the function defined by f (x) = sin (x2) is a continuous function.Given π(π₯) = sinβ‘(π₯^2 ) Let π(π) = sinβ‘π₯ & π(π) = π₯^2 Now, (π π π)(π) = g(β(π₯)) = π(π₯^2 ) = sinβ‘(π₯^2 ) = π(π) So, we can write π(π₯) = ππβ Here, π(π₯) = sinβ‘π₯ is continuous & β(π₯) = π₯^2 is continuous being a polynomial . We know that if two function π & β are continuous then their composition πππ is continuous Hence, ππβ(π₯) is continuous β΄ π(π) is continuous .
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About the Author
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 and Computer Science at Teachoo