Provide an appropriate response.
-Identify the incorrect statements about limits.
I. The number $L$ is the limit of $f ( x )$ as $x$ approaches $c$ if $f ( x )$ gets closer to $L$ as $x$ approaches $x _ { 0 }$ .
II. The number $L$ is the limit of $f ( x )$ as $x$ approaches $c$ if, for any $\varepsilon > 0$ , there corresponds a $\delta > 0$ such that $\mid f ( x ) - L$ $\varepsilon$ whenever $0 < | x - c | < \delta$ .

III. The number $L$ is the limit of $f ( x )$ as $x$ approaches $c$ if, given any $\varepsilon > 0$ , there exists a value of $x$ for which $\mid f ( x )$ $\varepsilon .$

Question

Provide an appropriate response.
-Identify the incorrect statements about limits.
I. The number

L

is the limit of

f ( x )

as

x

approaches

c

if

f ( x )

gets closer to

L

as

x

approaches

x _ { 0 }

.
II. The number

L

is the limit of

f ( x )

as

x

approaches

c

if, for any

\varepsilon > 0

, there corresponds a

\delta > 0

such that

\mid f ( x ) - L

\varepsilon

whenever

0 < | x - c | < \delta

.

III. The number

L

is the limit of

f ( x )

as

x

approaches

c

if, given any

\varepsilon > 0

, there exists a value of

x

for which

\mid f ( x )

\varepsilon .

Quizplus · Accepted Answer

Statement I is incorrect because it mistakenly refers to $x$ approaching $x_0$ instead of $c$. Statement III is incorrect because it misrepresents the formal definition of a limit, suggesting a specific value of $x$ satisfies the condition rather than all $x$ within a certain range. Statement II, despite a typographical error, closely resembles the correct formal definition of a limit.

Provide an Appropriate Response LLL Is the Limit Of f(x)f ( x )f(x)

Provide an Appropriate Response $L$ Is the Limit Of $f ( x )$