Let ​ Use a Riemann Sum with Four Subintervals

question 289

Multiple Choice

Let ​ Use a Riemann sum with four subintervals of equal length ( ) to approximate the area of R (under the graph of f on the interval [0, 2]) . Choose the representative points to be the left end points of the subintervals.
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Repeat previous part with eight subintervals of equal length ( ) .
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Compare the approximations obtained in previous parts with the exact area (4 sq units) . Do the approximations improve with larger n?
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• A) 4.8 sq units; 4.4 sq units; yes
• B) 4.4 sq units; 4.8 sq units; yes
• C) 4.8 sq units; 4.4 sq units; no
• D) 4.4 sq units; 4.8 sq units; no

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Definitions:

Orbit

The bony cavity containing the eyeball and its associated muscles, nerves, and blood vessels.

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An infection or inflammation of the conjunctiva, often characterized by redness, itching, and watering of the eyes.

Dacryocystitis

An infection of the tear sac (dacryocyst) at the corner of the eye, leading to inflammation and often blockage of the tear duct.

Lacrimal Passage

A drainage system for tears from the eye into the nasal cavity, which includes the lacrimal ducts and sac.