(6). The fanction \( f \) has confinnous second derivative, and a crifical poing of \( (-10,-2) \) suppose \( f_{x x}(-10,-2)=-20 \), \( f_{x y}(-10,-2)=-10 \) \( f_{y y}(-10,-2)=-5 \). Then the poing \( (-10,-2) \)

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

Let \( (M):\left(2 y^{2}+3 x\right) d x+(2 x y) d y=0 \). Then None of the mentioned \( (M) \) is a non-exact ODE and \( x \) is an integrating factor. \( (M) \) is a non-exact ODE and \( y \) is an integrating factor. \( (M) \) is an exact ODE

Evaluate the following integral: \[ \int_{0}^{\infty} 4^{-x} d x \]

\( Z = \int _ { X } ^ { y } e ^ { t ^ { 2 } } d t \)

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