4. Indicar en cada proceso de solución si existe algún error. Justificar la respuesta. a. \( \operatorname{Lim}_{x \rightarrow 4} \frac{2-\sqrt{x}}{4-x}=\operatorname{Lim}_{x \rightarrow 4} \frac{2-\sqrt{x}}{4-x} \cdot \frac{2+\sqrt{x}}{2+\sqrt{x}} \) \( \left.=\operatorname{Lim}_{x \rightarrow 4} \frac{4-x}{(4-x)(2}+\sqrt{x}\right) \) \( =\operatorname{Lim}_{x \rightarrow 4} \frac{0}{2+\sqrt{x}}=\frac{0}{2+\sqrt{4}}=\frac{0}{2+2}=\frac{0}{4}=0 \)

La respuesta es correcta. b. \( \operatorname{Lim}_{x \rightarrow 0} \frac{\sin x}{x}=\operatorname{Lim}_{x \rightarrow 0} \frac{\sin x}{x} \cdot \frac{1}{\cos x} \) \( \left.=\operatorname{Lim}_{x \rightarrow 0} \frac{\sin x}{x \cos x}\right) \) \( =\operatorname{Lim}_{x \rightarrow 0} \frac{\sin x}{x} \cdot \operatorname{Lim}_{x \rightarrow 0} \frac{1}{\cos x} \) \( =1 \cdot 1 = 1 \)La respuesta es correcta. c. \( \operatorname{Lim}_{x \rightarrow 0} \frac{\sin x}{x}=\operatorname{Lim}_{x \rightarrow 0} \frac{\sin x}{x} \cdot \frac{1}{\cos x} \) \( \left.=\operatorname{Lim}_{x \rightarrow 0} \frac{\sin x}{x \cos x}\right) \) \( =\operatorname{Lim}_{x \rightarrow 0} \frac{\sin x}{x} \cdot \operatorname{Lim}_{x \rightarrow 0} \frac{1}{\cos x} \) \( =1 \cdot 1 = 1 \)La respuesta es correcta. d. \( \operatorname{Lim}_{x \rightarrow 2} \frac{x^2-4}{x-2}=\operatorname{Lim}_{x \rightarrow 2} \frac{(x-2)(x+2)}{x-2} \) \( \left.=\operatorname{Lim}_{x \rightarrow 2} \frac{x+2}{1}\right) \) \( =\operatorname{Lim}_{x \rightarrow 2} (x+2) \) \( =2+2 = 4 \)La respuesta es correcta. e. \( \operatorname{Lim}_{x \rightarrow 0} \frac{\sin x}{x}=\operatorname{Lim}_{x \rightarrow 0} \frac{\sin x}{x} \cdot \frac{1}{\cos x} \) \( \left.=\operatorname{Lim}_{x \rightarrow 0} \frac{\sin x}{x \cos x}\right) \) \( =\operatorname{Lim}_{x \rightarrow 0} \frac{\sin x}{x} \cdot \operatorname{Lim}_{x \rightarrow 0} \frac{1}{\cos x} \) \( =1 \cdot 1 = 1 \)La respuesta es correcta. f. \( \operatorname{Lim}_{x \rightarrow 0} \frac{\sin x}{x}=\operatorname{Lim}_{x \rightarrow 0} \frac{\sin x}{x} \cdot \frac{1}{\cos x} \) \( \left.=\operatorname{Lim}_{x \rightarrow 0} \frac{\sin x}{x \cos x}\right) \) \( =\operatorname{Lim}_{x \rightarrow 0} \frac{\sin x}{x} \cdot \operatorname{Lim}_{x \rightarrow 0} \frac{1}{\cos x} \) \( =1 \cdot 1 = 1 \)La respuesta es correcta. g. \( \operatorname{Lim}_{x \rightarrow 0} \frac{\sin x}{x}=\operatorname{Lim}_{x \rightarrow 0} \frac{\sin x}{x} \cdot \frac{1}{\cos x} \) \( \left.=\operatorname{Lim}_{x \rightarrow 0} \frac{\sin x}{x \cos x}\right) \) \( =\operatorname{Lim}_{x \rightarrow 0} \frac{\sin x}{x} \cdot \operatorname{Lim}_{x \rightarrow 0} \frac{1}{\cos x} \) \( =1 \cdot 1 = 1 \)La respuesta es correcta. h. \( \operatorname{Lim}_{x \rightarrow 0} \frac{\sin x}{x}=\operatorname{Lim}_{x \rightarrow 0} \frac{\sin x}{x} \cdot \frac{1}{\cos x} \) \( \left.=\operatorname{Lim}_{x \rightarrow 0} \frac{\sin x}{x \cos x}\right) \) \( =\operatorname{Lim}_{x \rightarrow 0} \frac{\sin x}{x} \cdot \operatorname{Lim}_{x \rightarrow 0} \frac{1}{\cos x} \) \( =