Let F(x) = 8x Use a Riemann Sum with Four

question 3

Multiple Choice

Let f(x) = 8x Use a Riemann sum with four subintervals of equal length (n = 4) 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.
Repeat previous part with eight subintervals of equal length (n = 8) .
Compare the approximations obtained in previous parts with the exact area (16 sq units) . Do the approximations improve with larger n?

• A) 14 sq units; 12 sq units; yes
• B) 14 sq units; 12 sq units; no
• C) 12 sq units; 14 sq units; no
• D) 12 sq units; 14 sq units; yes

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Definitions:

Regio-

A prefix indicating the region or position in a molecule where a chemical reaction occurs, often critical in determining the outcome of synthesis.

Meso Dibromide

A meso compound formed by the dibromination of an alkene, exhibiting optical inactivity due to internal symmetry.

(E)-Hex-3-Ene

A linear six-carbon compound with a double bond between the third and fourth carbons in the E (trans) configuration.

Enantiomeric Dibromides

Compounds that are mirror images of each other, each containing two bromine atoms attached to a carbon-based skeleton.