Mathematics

Problem

A piecewise function

g

is defined by

g(x)=2

for

x<3

and

g(x)=-1

for

x\ge 3

. Which statement best accounts for why

\displaystyle \lim_{x\to 3}g(x)

does not exist? a) The limit fails because

g(3)\neq 2

, so the function value and the approaching value are different. b) The limit fails simply because

g

is not continuous at

x=3

. c) The limit fails because the left‐hand and right‐hand limits approach different finite numbers. d) The limit fails because the function becomes unbounded as

x

approaches

3

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