Let P = lim x → 0 + 1 + tan 2 x 1 2 x , then log P is equal to

Step-by-step solution

Let P = 1 + tan 2 x 1 2 x             ( 1 ∞ form ) If l = lim x → a f x g x , where lim x → a f x → 1 and lim x → a g x → ∞ , then l = e lim x → a f x - 1 · g x ⇒   P = e lim x → 0 + 1 + tan 2 x - 1 · 1 2 x ⇒   P = e lim x → 0 + 1 2 tan x x 2 Using lim x → 0 tan x x = 0 , we get P = e 1 2 ⇒   log P = log e 1 2 = 1 2 .