Provide an Appropriate Response $\varepsilon > 0$ , Find an Interval $I = ( 5 - \delta , 5 ) , \delta > 0$

question 192

Multiple Choice

Provide an appropriate response.
-Given $\varepsilon > 0$ , find an interval $I = ( 5 - \delta , 5 ) , \delta > 0$ , such that if $x$ lies in $I$ , then $\sqrt { 5 - x } < \varepsilon$ . What limit is being verified and what is its value?

• A) \(\lim _ { x \rightarrow 5 ^ { - } } \sqrt { x } = 5\)
• B) \(\lim _ { x - 5 ^ { + } } \sqrt { 5 - x } = 0\)
• C) \(\lim _ { x \rightarrow 0 ^ { - } } \sqrt { 5 - x } = 0\)
• D) \(\lim _ { x \rightarrow 5 ^ { - } } \sqrt { 5 - x } = 0\)

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Definitions:

Western Territories

Regions in the western part of the United States or other countries that are not yet fully incorporated into the main political structure.

Political Equals

Political equals refer to individuals or entities possessing the same rights and responsibilities within a political system, emphasizing equality before the law and in the democratic process.

Alexander Hamilton

A founding father of the United States, first Secretary of the Treasury, and influential in the creation of the national banking system and economic policy.

Anti-Federalist

Opponents of the ratification of the U.S. Constitution in the late 18th century, favoring a weaker central government and greater state autonomy.