Question
31. \( \lim _{x \rightarrow-3}\left(x^{3}-3 x\right) \)
Ask by Whittaker Vaughn. in Thailand
Mar 21,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The limit is -18.
Solution
Find the limit \( \lim_{x\rightarrow -3} (x^3-3x) \).
Evaluate the limit by following steps:
- step0: Evaluate the limit:
\(\lim _{x\rightarrow -3}\left(x^{3}-3x\right)\)
- step1: Rewrite the expression:
\(\lim _{x\rightarrow -3}\left(x^{3}\right)-\lim _{x\rightarrow -3}\left(3x\right)\)
- step2: Calculate:
\(-27-\left(-9\right)\)
- step3: Calculate:
\(-18\)
The limit of \(x^3 - 3x\) as \(x\) approaches -3 is -18.
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Simplify this solution The Deep Dive
To evaluate the limit \( \lim _{x \rightarrow -3} \left(x^{3}-3x\right) \), we can substitute \( x = -3 \) directly into the expression. Calculating: \[ (-3)^{3} - 3 \cdot (-3) = -27 + 9 = -18 \] Therefore, \[ \lim _{x \rightarrow -3}\left(x^{3}-3 x\right) = -18. \] And there you have it, the limit is \(-18\)!
