\( \lim _ { x \rightarrow 0 } \frac { 3 x ^ { 2 } \sin x + x \tan 5 x } { x ^ { 2 } - 2 \tan 3 x ^ { 2 } } \)

- Derivative of \( \tan x \) Solution

Deriva. \( \frac{4}{x} \)

Determine the distance traveled by a particle moving along the curve \( y = \sin(x) \) from \( x = 0 \) to \( x = \pi \).

Calculate the volume obtained by revolving the area between \( y = \frac{1}{x} \), \( y = 0 \), and \( x = 1 \) to \( x = 2 \) around the y-axis using the disc method.

The area of a rectangular cross-section of a solid is given by the dimensions in terms of a linear function: width = \(x\) and height = \(3 - x\) for \(0 \leq x \leq 3\). Calculate the volume of the solid when these rectangles are stacked from \(x=0\) to \(x=3\).