If $\lim _ { x \rightarrow 2 ^ { + } } f ( x ) = 7.9$, then if $\lim _ { x \rightarrow 2 } f ( x )$ exists, to what value does it converge?
Select the correct answer.
A) $6.9$
B) $8.9$
C) $9.9$
D) $7.9$
E) $5.9$

Question

Quizplus · Accepted Answer

Since we are given that $\lim_{x \rightarrow 2^{+}} f(x) = 7.9$, we know that as $x$ approaches 2 from the right, $f(x)$ approaches 7.9. If the limit $\lim_{x \rightarrow 2} f(x)$ exists, then it must be the case that $f(x)$ approaches the same value whether $x$ approaches 2 from the left or the right. Therefore, the only possible value of $\lim_{x \rightarrow 2} f(x)$ is 7.9, since this is the only value that $f(x)$ approaches as $x$ approaches 2. Therefore, the correct answer is D.

If lim⁡x→2+f(x)=7.9\lim _ { x \rightarrow 2 ^ { + } } f ( x ) = 7.9limx→2+​f(x)=7.9

If $\lim _ { x \rightarrow 2 ^ { + } } f ( x ) = 7.9$