Find the limit.
-$$\lim _ { x \rightarrow 7 ^ { + } } \frac { 1 } { x + 7 }$$
A) $\infty$
B) 0
C) $\approx$
D) $- 1$

Question

Quizplus · Accepted Answer

As $x$ approaches 7 from the right, the denominator $x + 7$ approaches 14, making the fraction $\frac{1}{x+7}$ approach a small positive number, but never reaching 0. Thus, the limit does not approach infinity, zero, or -1 directly, but since the question seems to imply how the function behaves as it gets close to 14 in the denominator (not directly the limit to a specific value), the closest interpretation given the options would be that it's asking about the behavior as the denominator gets very small (approaching from the right of 7 makes the denominator approach 14, not a small number). However, the explanation provided seems to have misinterpreted the question's intention. The correct interpretation should be about the behavior as x approaches a value causing the denominator to become very small or approach zero, but in this case, since the denominator approaches 14, none of the options directly apply correctly. The explanation mistakenly suggests a scenario where the denominator approaches a value close to 0, which is not the case here. The correct answer should reflect the behavior of the function as x approaches 7 from the right, which would not lead to the denominator becoming small or the function approaching infinity. My initial explanation was incorrect due to a misunderstanding of the function's behavior in relation to the given options.

Find the Limit lim⁡x→7+1x+7\lim _ { x \rightarrow 7 ^ { + } } \frac { 1 } { x + 7 }x→7+lim​x+71​

Find the Limit $\lim _ { x \rightarrow 7 ^ { + } } \frac { 1 } { x + 7 }$