Example 13 - Discuss continuity of f(x) = {x, x2 - Examples

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  1. Chapter 5 Class 12 Continuity and Differentiability
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Example 13 Discuss the continuity of the function f given by 𝑓(π‘₯)={β–ˆ(& π‘₯, 𝑖𝑓 π‘₯β‰₯0@& π‘₯2 , 𝑖𝑓 π‘₯<0)─ 𝑓(π‘₯)={β–ˆ(& π‘₯, 𝑖𝑓 π‘₯β‰₯0@& π‘₯2 , 𝑖𝑓 π‘₯<0)─ Case 1 : At x = 0 f is continuous at x = 0 if, L.H.L = R.H.L = 𝑓(0) Also , 𝑓 (π‘₯)= π‘₯ So, 𝑓 (0)= 0 Case 2 Let c be any real number less than 0. So, π‘₯ =𝑐 where c<0 ∴ 𝑓(π‘₯)=π‘₯2 f is continuous at x = c if lim┬(x→𝑐) 𝑓(π‘₯)= 𝑓(𝑐) Thus, L.H.L = R.H.L = f(0) β‡’ f is continuous at π‘₯=0.

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