Ex. 3 : Évaluer les limites suiv a) \( \lim _{x \rightarrow 2} \frac{\sqrt{2}-\sqrt{x}}{x^{2}-3 x+2} \)

Calculate the limit \( \lim _{x \rightarrow 2} \frac{\sqrt{2}-\sqrt{x}}{x^{2}-3 x+2} \). Evaluate the limit by following steps: - step0: Evaluate using transformations: \(\lim _{x\rightarrow 2}\left(\frac{\sqrt{2}-\sqrt{x}}{x^{2}-3x+2}\right)\) - step1: Multiply by the Conjugate: \(\lim _{x\rightarrow 2}\left(\frac{1}{\left(\sqrt{2}+\sqrt{x}\right)\left(-x+1\right)}\right)\) - step2: Rewrite the expression: \(\frac{\lim _{x\rightarrow 2}\left(1\right)}{\lim _{x\rightarrow 2}\left(\left(\sqrt{2}+\sqrt{x}\right)\left(-x+1\right)\right)}\) - step3: Evaluate: \(\frac{1}{\lim _{x\rightarrow 2}\left(\left(\sqrt{2}+\sqrt{x}\right)\left(-x+1\right)\right)}\) - step4: Evaluate: \(\frac{1}{-2\sqrt{2}}\) - step5: Rewrite the fraction: \(-\frac{1}{2\sqrt{2}}\) - step6: Multiply by the Conjugate: \(\frac{-\sqrt{2}}{2\sqrt{2}\times \sqrt{2}}\) - step7: Multiply the numbers: \(\frac{-\sqrt{2}}{4}\) - step8: Calculate: \(-\frac{\sqrt{2}}{4}\) La limite de l'expression \( \lim _{x \rightarrow 2} \frac{\sqrt{2}-\sqrt{x}}{x^{2}-3 x+2} \) est égale à \( -\frac{\sqrt{2}}{4} \).