A Function $\mathrm { f } ( \mathrm { x } )$

question 59

Multiple Choice

A function $\mathrm { f } ( \mathrm { x } )$ , a point $\mathrm { c }$ , the limit of $\mathrm { f } ( \mathrm { x } )$ as $x$ approaches $\mathrm { c }$ , and a positive number $\varepsilon$ is given. Find a number $\delta > 0$ such that for all $x , 0 < | \mathrm { x } - \mathrm { c } | < \delta \Rightarrow | \mathrm { f } ( \mathrm { x } ) - \mathrm { L } | < \varepsilon$ .
- $$f ( x ) = \frac { x ^ { 2 } + - 16 x + 60 } { x + - 6 } , c = 6 , \varepsilon = 0.02$$

• A) \(\mathrm { L } = 0 ; \delta = 0.02\)
• B) \(L = - 20 ; \delta = 0.03\)
• C) \(\mathrm { L } = - 16 ; \mathrm { \delta } = 0.03\)
• D) \(\mathrm { L } = - 4 ; \mathrm { \delta } = 0.02\)

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Definitions:

Main Group Non-metal

Elements located in the s and p blocks of the periodic table, excluding metalloids and metals, essential for various biological and industrial processes.

Transition Metal Elements

Elements found in groups 3 through 12 of the periodic table, characterized by their ability to form stable compounds with variable oxidation states.

Ionic

Relating to or involving ions, typically describing chemical bonds formed through the electrostatic attraction between oppositely charged ions.

Coordinate Covalent

A type of chemical bond where both electrons come from the same atom, typically seen in complex ions or molecules where a metal atom is bonded to one or more ligands.