Question

`lim_(x→0) (sin^2x)/(sqrt(2) - sqrt(1 + cos))` equals ______.

विकल्प

• `sqrt(2)`

• `4sqrt(2)`

• 4

• `2sqrt(2)`

Answer 1

`lim_(x→0) (sin^2x)/(sqrt(2) - sqrt(1 + cos))` equals `underlinebb(4sqrt(2))`.

Explanation:

`lim_(x→0) (sin^2x)/(sqrt(2) - sqrt(1 + cos))`    `(0/0)`form

'L' Hospital Rule

`lim_(x→0) (2sinxcosx)/(0 - 1/2 ((-sinx))/sqrt(1 + cosx))`

= `4sqrt(2)`