If \( z=x \cdot f\left(\frac{y}{x}\right)+y\left(\frac{y}{x}\right) \cdot S \cdot T \cdot \cdot x \frac{\partial z}{\partial x}+ \) \( y \cdot \frac{\partial z}{\partial y}=x \cdot f(y / x) \)

3.- \( \quad f(x)=x \ln \cos x \)

52. \( \star \sum_{n=1}^{\infty} \sqrt{n}(\sin n)\left(\sin \frac{1}{n}\right)^{2} \)

\( \sum _ { y = 1 } ^ { n } \sum _ { x = 1 } ^ { n } 4 x + 7 y + x ^ { 2 } \)

Label each expression as a scalar quantity, a vector quantity or undefined, if \( f \) is a scalar function and \( F \) is a vector field. \( \nabla \times(\nabla f) \) scalar vector

Evaluate the line integral \( \int_{C} 5 x d s \), where \( C \) is the line segment from \( (1,2) \) to \( (8,7) \). \( \int_{C} 5 x d s=\square \)