Question32. $\lim _{x \rightarrow 0} \frac{\sqrt{2-x}-\sqrt{2}}{2 x}$

Studdy Solution
Now, evaluate the limit as $x$ approaches 0:
$$\lim _{x \rightarrow 0} \frac{-1}{2(\sqrt{2-x}+\sqrt{2})} = \frac{-1}{2(\sqrt{2-0}+\sqrt{2})} = \frac{-1}{2(2\sqrt{2})} = \frac{-1}{4\sqrt{2}}$$
To simplify further, multiply the numerator and the denominator by $\sqrt{2}$:
$$\frac{-\sqrt{2}}{8}$$
The value of the limit is:
$$\boxed{\frac{-\sqrt{2}}{8}}$$