Estimating with Finite Sums Homework

Directions: Write legibly and in pencil. Complete the homework on time and by yourself. For each problem, write the instructions, label the solution, show all steps, and write the final answer in a sentence. Do not turn in your scratch work. Staple your pages together, in the correct order, and use this page as a cover sheet.

(1) Use finite approximations to estimate the area under the graph of between and

(2) Use finite approximations to estimate the area under the graph of between and

(3) Using rectangles whose height is given by the value of the function at the midpoint of the rectangle's base (the midpoint rule) estimate the area under the graph of the function between and using first two and then four rectangles.

(4) Using rectangles whose height is given by the value of the function at the midpoint of the rectangle's base (the midpoint rule) estimate the area under the graph of the function between and using first two and then four rectangles.

(5) An object is shot straight upward from sea level with an initial velocity of (a) Assuming that gravity is the only force acting on the object, give an upper estimate for its velocity after 5 sec have elapsed. Use for the gravitational acceleration. (b) Find a lower estimate for the height attained after 5 sec.  

(6) Use a finite sum to estimate the average of on the closed bounded interval by partitioning the interval into four subintervals of equal length and evaluating at the subinterval midpoints.

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