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

19. Find critical points of \( f(x, y, z)=x y+y z \) with constraints \( x^{2}+y^{2}=8 \) dan \( y z=8 \)

A car's velocity is given by the function \( v(t) = 5t^2 + 3 \). Calculate the distance traveled by the car from time \( t = 0 \) to \( t = 4 \).

\( \left. \begin{array} { l l } { y ^ { \prime } - y = 0 } & { y ( 0 ) = 0 } \\ { } & { y ^ { \prime } ( 0 ) = 1 } \\ { } & { y ^ { \prime \prime } ( 0 ) = 0 } \\ { } & { y ^ { \prime \prime } ( 0 ) = 0 } \end{array} \right. \)

3. Hitung luas daerah yang dibatasi oleh kurva \( y=x^{2} \) dan \( y=4 x-x^{2} \)

Berilgan qatorlarni absolyut va shartli yaqinlashishga tekshiring. \[ \sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{(n+1) \ln (n+1)} \]