For the function

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

Problem

For the function

g(x)=\dfrac{2x^{3}-x+1}{x^{2}+4}

, evaluate the one-sided limits at

x=1

. (i)

\displaystyle \lim_{x\to 1^{-}} g(x)

(ii)

\displaystyle \lim_{x\to 1^{+}} g(x)

(iii) Hence, state the value of

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

, giving reason.