Исследовать ряд на сходимость, используя признак Даламбера

3. find taylor series of (2 Points) * \( \begin{array}{l}f(x)=e^{x} \cos x \quad \text { at } x=0 \\ f(x)=1+x-\frac{2 x^{3}}{3!}+\ldots \\ f(x)=1+x-\frac{x^{3}}{3!}+\ldots \\ f(x)=1+x-\frac{x^{2}}{2!}+\ldots \\ f(x)=1+x-\frac{2 x^{2}}{2!}+\ldots\end{array} \)

2. find Maclurin expansion of (2 Points) * \[ \begin{array}{l}f(x)=\sinh x \\ f(x)=1+\frac{x^{2}}{2!}+\frac{x^{4}}{4!}-\ldots \ldots \\ f(x)=x+\frac{x^{2}}{2!}+\frac{x^{3}}{3!}+\ldots \ldots \\ f(x)=x+\frac{x^{3}}{3}+\frac{x^{5}}{5}+\ldots \ldots \\ f(x)=x+\frac{x^{3}}{3!}+\frac{x^{5}}{5!}+\ldots\end{array} \]

6. find Maclurin expansion of (2 Points) * \( f(x)=e^{x}-1 \) \( f(x)=x-\frac{x^{2}}{2!}-\frac{x^{3}}{3!}-\ldots \) \( f(x)=x+\frac{x^{2}}{2!}+\frac{x^{3}}{3!}+\ldots \) \( f(x)=x-\frac{x^{2}}{2}-\frac{x^{3}}{3}-\ldots \). None of these

\( f ( x ) = \int | x | d x \)

Pregunta. 2.1 Determine los valores extremos de \( f(x, y)=x^{2}+2 y^{2} \), sujeto a la restricción \( x^{2}+y^{2}=1 \)