Question
1) \( \lim _{x \rightarrow-2}\left(3 x^{3}+5 x^{2}-1\right) \)
Ask by Colon Whittaker. in Saudi Arabia
Feb 20,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The limit is -5.
Solution
Calculate the limit \( \lim _{x \rightarrow-2}3x^3+5x^2-1 \).
Evaluate the limit by following steps:
- step0: Evaluate the limit:
\(\lim _{x\rightarrow -2}\left(3x^{3}+5x^{2}-1\right)\)
- step1: Rewrite the expression:
\(\lim _{x\rightarrow -2}\left(3x^{3}\right)+\lim _{x\rightarrow -2}\left(5x^{2}\right)-\lim _{x\rightarrow -2}\left(1\right)\)
- step2: Calculate:
\(-24+20-1\)
- step3: Calculate:
\(-4-1\)
- step4: Calculate:
\(-5\)
The limit of the function \(3x^3+5x^2-1\) as \(x\) approaches -2 is -5.
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Simplify this solution The Deep Dive
To evaluate the limit \( \lim _{x \rightarrow -2}\left(3 x^{3}+5 x^{2}-1\right) \), we can directly substitute \(-2\) into the polynomial. Calculating: \[ 3(-2)^{3} + 5(-2)^{2} - 1 = 3(-8) + 5(4) - 1 = -24 + 20 - 1 = -5. \] So, the limit is \(-5\). If you have a polynomial function, evaluating it at a point is usually as straightforward as substituting that value in, making limits like this one quite a breeze!
