Mathematics

Mathematics

Problem

A function

g

is defined for values of

x

close to 5 (but not at

x=5

). As

x

approaches 5 from the left, the

y

-values of

g

approach 2. As

x

approaches 5 from the right, the

y

-values of

g

approach

-1

. State the value of

\displaystyle \lim_{x\to5^-} g(x)

, the value of

\displaystyle \lim_{x\to5^+} g(x)

, and determine whether

\displaystyle \lim_{x\to5} g(x)

exists.

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