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

question 217

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 $x , 0 < | \mathrm { x } - \mathrm { c } | < \delta \Rightarrow | \mathrm { f } ( \mathrm { x } ) - \mathrm { L } | < \varepsilon$ .
- $$f ( x ) = \frac { 14 } { x } , c = 7 , \varepsilon = 0.4$$

• A) \(L = 2 ; \delta = 3.5\)
• B) \(L = 2 ; \delta = 1.75\)
• C) \(\mathrm { L } = 2 ; \delta = 1.17\)
• D) \(L = 2 ; \delta = 17.5\)

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Definitions:

Charge

In physics, charge refers to a property of matter that causes it to experience a force when near other electrically charged matter; there are two types, positive and negative, which attract each other.

Solvent

Liquid that holds another substance in solution.

Anion

Ion carrying a negative charge.

Positively Charged

Having more protons than electrons, resulting in a net positive electric charge.