Example 2 - Chapter 5 Class 12 Continuity and Differentiability

Last updated at August 17, 2026 by

Example 2 - Examine whether f(x) = x2 is continuous at x = 0 - Examples

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Example 2 Examine whether the function f given by 𝑓 (π‘₯) = π‘₯2 is continuous at π‘₯ = 0 𝑓(π‘₯) is continuous at π‘₯ = 0 if lim┬(xβ†’0) 𝑓(π‘₯) = 𝑓(0) L.H.S (π₯𝐒𝐦)┬(π±β†’πŸŽ) 𝒇(𝒙) "= " lim┬(xβ†’0) " " π‘₯2 Putting π‘₯ = 0 = (0)2 = 0 R.H.S 𝒇(𝟎) = (0)2 = 0 Since LHS = RHS Hence, f(x) is continuous at x = 0

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