Determine the value(s) of \( x \) for which \( f(x) \) is continuous it \( f(x)=\frac{3 x+\sin x}{\sqrt{2-x}} \)

If the equation \( (2 x-3 y) d x+(3 x-2 y) d y=0 \) is exact, what is the general solution?

2 Bestimmen Sie die Koordinaten der Extrempunkte des Graphen von \( f \). \( \begin{array}{lll}\text { a) } f(x)=2 x-e^{x} & \text { b) } f(x)=x \cdot e^{x} & \text { c) } f(x)=x \cdot e^{-x} \\ \text { d) } f(x)=x^{2} \cdot e^{2 x} & \text { e) } f(x)=e^{3 x}-6 x & \text { f) } f(x)=\left(x^{2}-3\right) \cdot e^{x}\end{array} \)

\( \sum _ { n = 2 } ^ { \infty } \frac { \log ( ( 1 + \frac { 1 } { n } ) ^ { n } ( 1 + n ) ) } { ( \log n ^ { n } ) ( \log ( n + 1 ) ^ { n + 1 } ) } : \log _ { 2 } \sqrt { e } \)

\( \sum _ { n = 2 } ^ { \infty } \frac { \log [ ( 1 + \frac { 1 } { n } ) ^ { n } ( t + n ) ] } { ( \log n ^ { n } ) ( \log ( n + 1 ) ^ { n + 1 } ) } \)

What does the Fundamental Theorem of Calculus state about the relationship between differentiation and integration?