Derivative of \( x^{x^{x}} ? \)

b) \( y=\frac{x-1}{x^{2}+2 x+3} \)

Evaluate the following triple integral in spherical coordinated. \[ f(\rho, \theta, \varphi)=\sin (\varphi) \text {. } \] over the region \( 0 \leq \theta \leq 2 \pi, 0 \leq \varphi \leq \frac{\pi}{4}, 8 \leq \rho \leq 9 \)

Find the volume of the solid formed by rotating the area under the curve \( y = \frac{1}{x} \) from \( x = 1 \) to \( x = 3 \) about the y-axis.

\( \frac { 1 } { 1 \cdot 2 } + \frac { 1 } { 2 \cdot 3 } + \frac { 1 } { 3 \cdot 4 } + \ldots + \frac { 1 } { 999 \cdot 1000 } \)

Evaluate the triple integral. \[ \iiint_{G} x y \sin (y z) d V \text {, } \] where \( G \) is the rectangular box defined by the inequalities \( 0 \leq x \leq \pi, 0 \leq y \leq 17,0 \leq z \leq \frac{\pi}{102} \)