Determine Whether Each of the Following Statements Is True or False

question 82

Essay

Determine whether each of the following statements is true or false. If the statement is true, provide an appropriate justification. If the statement is false, provide a counterexample.(a) If $f ( x ) \neq 0 \text { on } [ a , b ] \text { then } \int _ { a } ^ { b } f ( x ) d x \neq 0$ (b) If $f$ is continuous on an interval containing a,b, and c, then $\int _ { a } ^ { b } f ( x ) d x = \int _ { a } ^ { c } f ( x ) d x - \int _ { b } ^ { c } f ( x ) d x$ (c) If $\int _ { a } ^ { b } f ( x ) d x \geq 0 , \text { then } f ( x ) \geq 0 \text { on } [ a , b ]$

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Definitions:

Elastic

Describes a situation where the quantity demanded or supplied of a product changes significantly in response to a change in price.

Illinois Central Railroad

A historic American railroad that operated in the central United States, particularly known for its role in the development of the railway network from the Great Lakes to the Gulf of Mexico.

Demand

The quantity of a good or service that consumers are willing and able to purchase at various prices during a given period.

Elastic

A characteristic of demand or supply where a change in price leads to a significant change in the quantity demanded or supplied.