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Ex 5.1, 31 - Ex 5.1

Ex 5.1, 31 - Chapter 5 Class 12 Continuity and Differentiability - Part 2

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Ex 5.1, 31 Show that the function defined by 𝑓(π‘₯)=cos⁑(π‘₯^2 ) is a continuous function.𝑓(π‘₯) = cos⁑(π‘₯^2 ) Let π’ˆ(𝒙) = cos⁑π‘₯ & 𝒉(𝒙) = π‘₯^2 Now, π’ˆπ’π’‰(𝒙) = g(β„Ž(π‘₯)) = 𝑔(π‘₯^2 ) = cos⁑(π‘₯^2 ) = 𝒇(𝒙) Hence, 𝑓(π‘₯) = π‘”π‘œβ„Ž(π‘₯) We know that π’ˆ(𝒙) = cos⁑π‘₯ is continuous as cos x is always continuous & 𝒉(𝒙) = π‘₯^2 is continuous as it is a polynomial Hence, 𝑔(π‘₯) & β„Ž(π‘₯) are both continuous . We know that If two function of 𝑔(π‘₯) & β„Ž(π‘₯) both continuous, then their composition π’ˆπ’π’‰(𝒙) is also continuous Hence, 𝒇(𝒙) is continuous .

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