Using rectangles of unit width on the interval [3,5], arrange the curves in ascending order of the estimated areas under them. (
Screenshot attached)
1 answer:
The areas can be estimated by adding the function values at the midpoints of the intervals 3–4 and 4–5. Those midpoints are x = 3.5 and x = 4.5. Hence we can approximate the area by adding f(3.5) and f(4.5). That is what is done in the attachments.
Top to bottom, the functions have approximate areas on the interval of ...
... 80, 77.5, 13.4, 50.5, 37.6, 58.325
Of course, the same graphing calculator can do numerical integration and give you the "exact" area (to 10 significant figures or better). The problem statement asks for this approximation, which is actually good enough for the purpose of ordering the values.
See the first attachment for results. See the other two attachments for area estimates and curve definitions (color key).
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Same as above. Plot the y-intercept (0, 4) and then use rise over run from the slope to plot (3, 5).
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You should end up with two PARALLEL lines. Since the lines never intersect, there are no solutions to this system of equations.
Answer: No Solution