Let $f(x) = 2x$ on the interval $1 ≤ x ≤ 3$.

1. Sketch a graph of the curve shading the area for approximating $A( f, 1 ≤ x ≤ 3)$.

2. Use sigma notation to write the sum for approximating the area under the curve using ten left endpoint rectangles. Will the approximation be an underestimate or an overestimate? Justify your answer.

   Steps (b):

   rectangle width: $(3 − 1)/10 = 0.2$
   $x_{0} = 1, x_{1} = 1.2, x_{2} = 1.4, ... x_{n} = \:?$

3. If right endpoint rectangles are used instead, will the approximation be an underestimate or an overestimate? Justify your answer.

   Hint (c):

   Make a sketch before deciding on your answer.