Which of the following statements is necessary and sufficient for to exist when you…

MATHEMATICS · Single correct · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Which of the following statements is necessary and sufficient for

\displaystyle \lim_{x\to c}f(x)

to exist when you examine a table of values for

f

near

x=c

? (a) The numerical values of

f(x)

become arbitrarily large in magnitude as

x

approaches

c

. (b) The value

f(c)

is defined. (c) The numerical values of

f(x)

approach the same single number from both the left and the right as

x

approaches

c

. (d) The numerical values of

f(x)

approach the same single number, but only from the right of

c