Question
1) \( \lim _{x \rightarrow-2}\left(3 x^{3}+5 x^{2}-1\right) \)
Ask by French Savage. in the United Kingdom
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The limit is \(-5\).
Solution
To evaluate the limit:
\[
\lim _{x \rightarrow -2} \left(3x^{3} + 5x^{2} - 1\right)
\]
Since the function \( f(x) = 3x^{3} + 5x^{2} - 1 \) is a polynomial, it is continuous everywhere. Therefore, the limit as \( x \) approaches \(-2\) is simply the value of the function at \( x = -2 \).
Let's compute it step by step:
\[
\begin{align*}
f(-2) &= 3(-2)^{3} + 5(-2)^{2} - 1 \\
&= 3(-8) + 5(4) - 1 \\
&= -24 + 20 - 1 \\
&= -5
\end{align*}
\]
**Therefore, the limit is:**
\[
-5
\]
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Simplify this solution Mind Expander
To find the limit \( \lim_{x \rightarrow -2} \left(3 x^{3} + 5 x^{2} - 1\right) \), simply substitute \( -2 \) for \( x \) in the expression. Calculating it step-by-step: 1. \( 3(-2)^{3} = 3 \cdot (-8) = -24 \) 2. \( 5(-2)^{2} = 5 \cdot 4 = 20 \) 3. So, now combine these with \( -1 \): \[ -24 + 20 - 1 = -24 + 20 - 1 = -5 \] Thus, the limit is \( \lim_{x \rightarrow -2} \left(3 x^{3}+5 x^{2}-1\right) = -5 \).
