(24.) \( f(x)=\ln \left(\frac{1+\sqrt{x}}{1-\sqrt{x}}\right) \)

(b) Prove that \( \left|x_{n}-x_{n+1}^{\infty}\right|=\frac{1}{2^{n-1}} \) for all \( n \in \mathbb{N} \)

\( F(x)=\int_{1}^{\pi} \frac{\cos t}{t} d t \) siendo \( x \geq 1 \)

25) \( \lim _{x \rightarrow 0} \frac{|x-2|}{x-2}= \) ? \( \begin{array}{lllll}\text { A) }-\infty & \text { B) Limit yoktur } & \text { C) } 1 & \text { D) } \infty & \text { E) }-1\end{array} \)

24) \( \lim _{x \rightarrow 4} \frac{2-\sqrt{x}}{x^{2}-16}= \) ? \( \begin{array}{lllll}\text { A) }-\infty & \text { B) } \frac{1}{32} & \text { C) } 0 & \text { D) }-\frac{1}{32} & \text { E) Limit yoktur }\end{array} \)

b) (i) Consider the infinite geometric series \( \sum_{n=1}^{\infty} 10\left(1-\frac{3 x}{2}\right)^{n} \) for what does a sum to infinity exist? (ii) Find the sum of the seriec if.