(a) use the definition to find an expression for the area under the curve y = x3 from 0 to 1 as a limit. lim n→∞ n i = 1 (b) the following formula for the sum of the cubes of the first n integers is proved in appendix e. use it to evaluate the limit in part (a). 13 + 23 + 33 + + n3 = n(n + 1) 2 2

First work with stencil one. use a combination of reflections, rotations, and translations to see whether stencil one will overlap with the original pattern. list the sequence of rigid transformations you used in your attempt, noting the type of transformation, the direction, the coordinates, and the displacement in