Question
Evaluate the limit \( \lim _{x \rightarrow-3} \frac{4 x+36}{3-x} \)
Ask by Luna Adkins. in the United States
Feb 03,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The limit is 4.
Solution
To evaluate the limit:
\[
\lim_{x \rightarrow -3} \frac{4x + 36}{3 - x}
\]
**Step 1: Substitute \( x = -3 \) into the expression**
\[
\frac{4(-3) + 36}{3 - (-3)} = \frac{-12 + 36}{3 + 3} = \frac{24}{6} = 4
\]
**Step 2: Conclusion**
Since substituting \( x = -3 \) into the expression yields a finite value, the limit is:
\[
\boxed{4}
\]
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Simplify this solution The Deep Dive
To evaluate the limit \[ \lim _{x \rightarrow -3} \frac{4x + 36}{3 - x}, \] we first substitute \( x = -3 \) directly into the expression: \[ \frac{4(-3) + 36}{3 - (-3)} = \frac{-12 + 36}{3 + 3} = \frac{24}{6} = 4. \] Since the direct substitution yields a determinate form, we conclude that the limit exists and is equal to \[ \boxed{4}. \]
