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JEE Advanced Mathematics question

MathematicsContinuity and DifferentiabilityJEE Advanced

The function , is continuous at . Then

Answer: (A),(B)

Solution

Write and expand :

f(x)===(1+Missing argument for \tfrac\tfrac23x)(1-x)+=1-Missing argument for \tfrac\tfrac13x+.

(The same expansion holds for .) Hence

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Question ID VK-109340