Let . Which one of the following statements about the value of and is…

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

Problem

Let

f(x)=\dfrac{x^{2}-4}{x+3}

. Which one of the following statements about the value of

\displaystyle \lim_{x\to 1} f(x)

and

f(1)

is correct? (a)

\displaystyle \lim_{x\to 1} f(x)

exists but is not equal to

f(1)

. (b) Neither

\displaystyle \lim_{x\to 1} f(x)

nor

f(1)

exists. (c) Both

\displaystyle \lim_{x\to 1} f(x)

and

f(1)

exist and are equal. (d)

\displaystyle \lim_{x\to 1} f(x)

does not exist but

f(1)

exists.