\( \int e ^ { - \alpha t } \cos \beta t + \sin \beta t \)

2) \( \left.\frac{d}{d x} \cot ^{-1}(a x+b)\right|_{x=-b / a}=? \) A) \( a \) B) \( b \) C) \( -a \) D) \( -b \) E) \( a / b \)

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

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.

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