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

Question

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 $x , 0 < | \mathrm { x } - \mathrm { c } | < \delta \Rightarrow | \mathrm { f } ( \mathrm { x } ) - \mathrm { L } | < \varepsilon$.
-$f ( x ) = \sqrt { x + 2 } , L = 3 , c = 7$, and $\varepsilon = 1$
A) $\delta = 16$
B) $\delta = 4$
C) $\delta = 5$
D) $\delta = 7$

Quizplus · Accepted Answer

The Answer of 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 $x , 0 < | \mathrm { x } - \mathrm { c } | < \delta \Rightarrow | \mathrm { f } ( \mathrm { x } ) - \mathrm { L } | < \varepsilon$.
-$f ( x ) = \sqrt { x + 2 } , L = 3 , c = 7$, and $\varepsilon = 1$
A) $\delta = 16$
B) $\delta = 4$
C) $\delta = 5$
D) $\delta = 7$

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

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