# Example 13 - Chapter 5 Class 12 Continuity and Differentiability

Last updated at Dec. 8, 2016 by Teachoo

Last updated at Dec. 8, 2016 by Teachoo

Transcript

Example 13Discuss the continuity of the function f given by π(π₯)={β(& π₯, ππ π₯β₯0@& π₯2 , ππ π₯<0)β€ π(π₯)={β(& π₯, ππ π₯β₯0@& π₯2 , ππ π₯<0)β€ Case 1 : At x = 0 f is continuous at x = 0 if, L.H.L = R.H.L = π(0) Also , π (π₯)= π₯ So, π (0)= 0 Case 2 Let c be any real number less than 0. So, π₯ =π where c<0 β΄ π(π₯)=π₯2 f is continuous at x = c if limβ¬(xβπ) π(π₯)= π(π) Thus, L.H.L = R.H.L = f(0) β f is continuous at π₯=0.

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About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.