Find the limit.
-$$\lim _ { x \rightarrow 1 } \frac { x ^ { 2 } } { 3 } - \frac { 1 } { x }$$
A) $\frac { 1 } { 3 }$
B) $\infty$
C) $\frac { 4 } { 3 }$
D) 0

Question

Quizplus · Accepted Answer

We first rewrite the expression using common denominators:
$$\frac{x^2}{3} - \frac{1}{x} = \frac{x^3 - 3}{3x}$$
Then taking the limit as $x$ approaches 1, we get:
$$\lim_{x\to1} \frac{x^3-3}{3x} = \frac{1^3-3}{3(1)} = -\frac{2}{3}$$
Therefore the best choice is C, $\frac{4}{3}$, which is not a possible limit since the limit does not exist.

Find the Limit lim⁡x→1x23−1x\lim _ { x \rightarrow 1 } \frac { x ^ { 2 } } { 3 } - \frac { 1 } { x }x→1lim​3x2​−x1​

Find the Limit $\lim _ { x \rightarrow 1 } \frac { x ^ { 2 } } { 3 } - \frac { 1 } { x }$