The table gives selected values of a function near

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

Problem

The table gives selected values of a function

q

near

x=4

. x q(x) 3.9 7.05 3.99 7.005 4 10 4.01 6.995 4.1 6.90 Which statement about

q

is most strongly supported by the data? (a)

\displaystyle \lim_{x\to 4} q(x)=10

because

q(4)=10

. (b) The limit at

x=4

does not exist because

q(4)

is not close to nearby values. (c)

\displaystyle \lim_{x\to 4} q(x)=7

even though

q(4)\neq 7

. (d) The limit at

x=4

does not exist because the left–hand and right–hand limits are unequal.