The value of lim x → 0 log ( 1 + x + x 2 ) + log ( 1 − x + x 2 ) sec x − cos x is equal to

Question

The value of lim x → 0 log ( 1 + x + x 2 ) + log ( 1 − x + x 2 ) sec x − cos x is equal to, − 1, 1, 0, 2

MARKS App · Accepted Answer

lim x → 0 log 1 + x + x 2 + log 1 - x + x 2 sec x - cos x = lim x → 0 log 1 + x 2 2 - x 2 1 - cos 2 x / cos x = lim x → 0 log 1 + x 2 + x 4 sin x tan x = lim x → 0 log 1 + x 2 1 + x 2 x 2 1 + x 2 · x 2 1 + x 2 · 1 sin x x · tan x x · x 2 = 1 as lim x → 0 log 1 + x x = 1

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