_ x 0 ((x + 2 x)^ 3 + 2(x + 2 x)^ 2 + 3 (x + 2cosx))/((x + 2)^ 3 + 2(x + 2)^ 2 + 3 (x + 2)))^ 100/x is equal to _____ .

JEE Main 2022 Mathematics question

+ 2cosx))/((x + + is equal to .

Answer: 1

Let a = x + 2cos x and b = x + 2. As , and , so the base tends to (8 + 8 + 3 sin 2)/(8 + 8 + 3 sin 2) = 1: the form is . The limit is with L = lim

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Question ID VK-034804