Question

`lim_(x→0) sqrt(1 - cosx)/(sqrt(2)x)` is ______.

पर्याय

• 1

• –1

• zero

• does not exist

Answer 1

`lim_(x→0) sqrt(1 - cosx)/(sqrt(2)x)` is does not exist.

Explanation:

`lim_(x→0) sqrt(1 - cosx)/(sqrt(2)x)`;

`lim_(x→0) sqrt(2sin^2x)/(sqrt(2)x)`

⇒ `lim_(x→0) |sinx|/x`  ...`[∵ lim_(x→0) sinθ/θ = 1]` 

The limit of above does not exist as

LHS = –1 ≠ RHL = 1