Which of the following equalities is required for a function to be continuous at the…

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

Problem

Which of the following equalities is required for a function

f

to be continuous at the left-hand endpoint

x=a

of the closed interval

[a,b]

? (a)

\displaystyle\lim_{x\to a^{-}} f(x)=f(a)

(b)

\displaystyle\lim_{x\to a} f(x)=f(a)

(c)

\displaystyle\lim_{x\to a^{+}} f(x)=f(a)

(d)

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

exists, irrespective of

f(a)