\( y=\frac{1}{1-3^{x}} \) funksiyani \( x=-1 \) va \( x=0 \) nuqtalarda uzluksizlikga tekshiring va uzilish turini aniqlang.

5. Question (2 Points) * The coefficient of \( x \) in Maclurin's series \( \exp \) ansion of \( e^{\sin x} \) is equal to .... 2 3 0

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

1) \( \lim _{x \rightarrow 0} \frac{\sin \left(e^{x}-1\right)-x-\frac{x^{2}}{2}}{x^{4}} \)

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

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