14. Demostrar que \( x=\cos x \) para alguna \( x \) en \( \left(0, \frac{\pi}{2}\right) \) 15. Demostrar que \( x 2^{x}=1 \) para alguna \( x \) en \( (0,1) \)

1. Using Stoke's Theorem, evaluate \( \int_{C} F \cdot d r \) where \( C \) is any closed surface enclosing a square region of the xy plane bounded by the lines \( x= \pm 2, y= \pm 5 \), where \( F=3 y x^{2} i+x^{2} j \)

2. Evaluate the integral \( \int_{0}^{1} \int_{0}^{z} \int_{0}^{1-y}(x y z) d x d y d z \)

1. Using Stoke's Theorem, evaluate \( \int_{C} F \cdot d r \) where \( C \) is any closed surface enclosing a square region of the xy plane bounded by the lines \( x= \pm 2, y= \pm 5 \), where \( F=3 y x^{2} i+x^{2} j \)

Find the average rate of change of \( g(x)=-4 x^{3}-5 \) from \( x=-1 \) to \( x=3 \)

1. Using Stoke's Theorem, evaluate \( \int_{C} F \cdot d r \) where \( C \) is any closed surface enclosing a square region of the xy plane bounded by the lines \( x= \pm 2, y= \pm 5 \), where \( F=3 y x^{2} i+x^{2} j \)