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

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

1) \( y=\cos ^{-1}(\sin x) \Rightarrow y^{\prime}=? \) A) \( -\frac{\cos x}{|\cos x|} \) B) \( \frac{\cos x}{|\cos x|} \) C) \( -\frac{\cos x}{\sqrt{1-x^{2}}} \) D) \( \frac{\cos x}{\sqrt{1-x^{2}}} \) E) \( -\frac{\sin x}{\sqrt{1-x^{2}}} \)

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

Find the area under the curve defined by \( f(x) = 2x + 1 \) between the points \( x = 1 \) and \( x = 3 \).