Consider the rational function .

MATHEMATICS · Multi-part · AP · Calculus AB · Limits and Continuity · Limits and Continuity

Problem

Consider the rational function

f(x)=\dfrac{5x^{2}-7}{x+3}

. (i) State the domain of

f(x)

. (ii) Is

f(x)

continuous at

x=2

? Give a reason for your answer. (iii) Without performing algebraic simplification, write the value of

\displaystyle \lim_{x\to 2} f(x)

and justify your answer.