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Calc H U7 Day 15 - Lab

Let [pic] . Consider the region bounded by the graph of f, the x-axis, and the line x=2.

Divide the interval [0,2] into 8 equal subintervals. Draw a picture to help answer the following:

Obtain a lower estimate for the area of the region by using the left endpoint of each interval.

Obtain an upper estimate for the area by using the right endpoint of each interval.

Find an approximation for the area that is better than either of the answers in a) and b).

2.) Bernhard Riemann V is planning to take a Sunday afternoon trip in his 1976 Mercedes Benz whose odometer broke when it turned over 200,000 miles. Being the descendant of the mathematician Georg Friedrich Bernhard Riemann (1826-1866), he decides to estimate the miles driven by recording his speed at various times during the trip. Because this is to be a restful trip and not a military drill, he does not plan to take readings at specified intervals of time, but only when he remembers to do so. HE takes a stopwatch to record the time intervals (in minutes) to make the calculations easier for himself (and consequently for you). The following table contains the data he collects during his trip. Approximately how far does he travel? Each speedometer reading (in mph) is made at some point during the time interval recorded.

Time interval |15 |25 |30 |15 |20 |35 |40 |20 |10 | |Speed |30 |45 |50 |25 |45 |55 |50 |35 |25 | | | | | | | | | | | | |

After finding out how far he has driven, Bernhard would like to know his average speed. Can you find it?

3.) Let f be the function graphed to the right:

Which of the following is the best estimate of [pic]?

a) -24 b) 9 c) 26 d) 38

4.) The graph of a function f is given in the figure to the right.

When asked to estimate [pic] to five decimal places for accuracy,

a group of calculus students submitted the following answers:

a) -4.57440 b) 4.57440 c) 45.74402 d) 457.44021

Although one of these responses is correct, the other three are “obviously” incorrect.

Using arguments your classmates would understand, identify the correct answer and explain why each of the others cannot be correct.

5. Given: [pic] , find the values of:

[pic]

6.) 5. Given: [pic]

Evaluate as many of the following as possible. If you cannot give an answer, admit it!

7.) Let f be a continuous function on the closed interval [0,2]. If [pic] , then the greatest possible value of [pic] is

a) 0 b) 2 c) 4 d) 8 e) 16

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