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Example 19 - Show that f(x) = sin (x2) is continuous - Examples

Example 19 - Chapter 5 Class 12 Continuity and Differentiability - Part 2

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Example 19 Show that the function defined by f (x) = sin (x2) is a continuous function.Given 𝑓(π‘₯) = sin⁑(π‘₯^2 ) Let π’ˆ(𝒙) = sin⁑π‘₯ & 𝒉(𝒙) = π‘₯^2 Now, (π’ˆ 𝒐 𝒉)(𝒙) = g(β„Ž(π‘₯)) = 𝑔(π‘₯^2 ) = sin⁑(π‘₯^2 ) = 𝒇(𝒙) So, we can write 𝑓(π‘₯) = π‘”π‘œβ„Ž Here, 𝑔(π‘₯) = sin⁑π‘₯ is continuous & β„Ž(π‘₯) = π‘₯^2 is continuous being a polynomial . We know that if two function 𝑔 & β„Ž are continuous then their composition π’ˆπ’π’‰ is continuous Hence, π‘”π‘œβ„Ž(π‘₯) is continuous ∴ 𝒇(𝒙) is continuous .

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.