Question
3. \( \lim _{x \rightarrow 3}\left(x^{2}+2\right) \) \( \begin{array}{llll}\text { A. } 15 & \text { B. } 12 & \text { C. } 13 & \text { D. } 11\end{array} \)
Ask by Wang Bartlett. in the Philippines
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The limit is 11, so the answer is D.
Solution
To evaluate the limit:
\[
\lim_{x \rightarrow 3} \left(x^{2} + 2\right)
\]
You can directly substitute \( x = 3 \) into the function since it's a polynomial, which is continuous everywhere.
\[
x^{2} + 2 = (3)^{2} + 2 = 9 + 2 = 11
\]
**Therefore, the correct answer is:**
**D. 11**
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
To solve the limit \( \lim _{x \rightarrow 3}\left(x^{2}+2\right) \), you simply substitute \( x \) with \( 3 \). Calculating it step-by-step: 1. Plug in \( x = 3 \): \( 3^2 + 2 = 9 + 2 = 11 \). Thus, the answer is \( \boxed{11} \).
