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

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 \( t = 4 \).

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

2. Hitung nilai integral berikut dengan batas-batas yang diberikan: \[ \int_{1}^{3}\left(2 x^{3}-4 x^{2}+x\right) d x \]

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

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