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Let p = lim x→0+ (1 + tan²(√x))^(1/2x) then log p is equal to

1. 2
2. 1
3. 1/2
4. 1/4

Correct answer: 1/2

Solution

To find log p, we first analyze the limit as x approaches 0 from the right. The expression inside the limit simplifies to e^(lim x→0+ (1/2x) log(1 + tan²(√x))). As x approaches 0, tan²(√x) approaches 0, and using the Taylor expansion, we find that log(1 + tan²(√x)) behaves like tan²(√x). This leads to the limit evaluating to 1/2, thus log p equals 1/2.

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