Approximations in Calculus

What does this picture represent?

• Left Riemann Sum

• Right Riemann Sum

• Middle Riemann Sum

• Trapezoidal Sum

For a function that is strictly increasing, a right hand Riemann Sum is which of the following:

• Overestimate
• Underestimate
• Unable to Determine
• Exact Solution

Based on the table, use a Right Riemann sum and 4 sub-intervals to estimate the Area under the curve. (Choose the correct set-up.)

• 5(3) + 1(4) + 2(5) + 1(7)

• 5(4) + 1(5) + 2(7) + 1(6)

• 5(3) + 6(4) + 8(5) + 9(7)

• 0(3) + 5(4) + 6(5) + 8(7)

Use a midpoint Riemann Sum to approximate the area between 0 to 3 with 3 subintervals.

• 14

• 7

• 26

• 11

• Average Value
• Net Area
• Total Area
• Average Rate of Change

Use a right Riemann Sum to approximate the area of the shaded area.

• 12

• 9

• 10

• 5

• 40
• 32
• 64
• 28

Find the trapezoidal sum, with three sub-intervals indicated by the table.

• 23 meters

• 16.5 meters

• 34 meters

• 28.5 meters

• 176

• 352

• 420

• 488

A Riemann Sum uses rectangles to

• approximate the area under a curve. The more rectangles, the better the approximation.

• approximate the area under a curve. The less rectangles, the better the approximation.

• approximate the area under a curve. The more rectangles, the worse the approximation.