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Evaluate the following limits (i) lim(...

Evaluate the following limits
(i) `lim_(x to (pi)/(2)) tan^(2) x [sqrt(2 sin^(2) x + 3 sin x + 4) - sqrt(sin^(2) x + 6 sin x + 2)]`
(ii) `lim_(theta to 0) (sqrt(1 + sin 3 theta) -1)/(ln(1 + tan 2theta))`
(iii) `lim_(x to 0) (sqrt(1 + x) - ""^(3)sqrt(1 + x))/(x)`
(iv) `lim_(phi to 0) (8)/(phi^(8)) (1 - cos (phi^(2))/(2) - cos (phi^(2))/(4) + cos (phi^(2))/(2). cos (phi^(2))/(4))`

A

`(1)/(10)`

B

` (1)/(11)`

C

`( 1)/(12`

D

` (1)/(8)`

Text Solution

Verified by Experts

The correct Answer is:
C
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