10) Use Newton's Method to approximate the real zero of the function in the interval \( [1 \), \( f(x)=x^{3}-x-2 \), use \( x_{1}=1.5 \). Find \( x_{2}, x_{3} \) and \( x_{4} \). Keep 5 decimal places for each \( x \) value.

Find the following limit or state that it does not exist \[ \lim _{x \rightarrow-1} \frac{4(2 x-2)^{2}-64}{x+1} \]

\( \int _ { - 1 } ^ { 1 } \frac { x \cos ^ { 2 } x } { 1 + x ^ { 2 } } d x \)

Given the following velocity function of an object moving along a line, find the position function with the given initial position.

Given the following velocity function of an object moving aiong a line, find the position function with the given initial position. \[ v(t)=2 \sqrt[3]{t}, s(0)=3 \] The position function is \( s(t)=\square \)

\( \int \frac { 3 x ^ { 5 } } { \sqrt { 7 - 12 x ^ { 6 } } } d x = \square \)