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## Homework Statement

i need to find the value of limit but its indeterminate and i cant use l'hospital's rule.

i multiplied nominator and denominator with [itex]\displaystyle\lim_{x\rightarrow 0^+} {\frac{\sqrt{2sin^{2}(x/2)+1+cos^2(x)}}{|x|}}[/itex] to get rid of square root. After get i tried to make some transforms to simplify something but i couldn find anything right.

## Homework Equations

This is the question:

[itex]

\displaystyle\lim_{x\rightarrow 0^+} {\frac{\sqrt{2sin^{2}(x/2)+1-cos^2(x)}}{|x|}}

[/itex]

## The Attempt at a Solution

this is the last step that i came.

[itex]

\displaystyle\lim_{x\rightarrow 0^+} {\frac{1-cos(x)+1-cos^{2}(x)}{|x|\sqrt{2sin^{2}(x/2)+1+cos^2(x)}}}

[/itex]