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1) \( \lim _{x \rightarrow-2}\left(3 x^{3}+5 x^{2}-1\right) \)

Ask by Warner Warner. in the United Kingdom
Jan 23,2025

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The limit is \(-5\).

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Bonus Knowledge

To find the limit \( \lim _{x \rightarrow -2}\left(3 x^{3}+5 x^{2}-1\right) \), we can directly substitute \( x = -2 \) into the polynomial function. Calculating step by step: 1. Substitute \( x = -2 \): \[ 3(-2)^3 + 5(-2)^2 - 1 \] 2. Calculate \( (-2)^3 = -8 \): \[ 3(-8) + 5(-2)^2 - 1 = -24 + 5(4) - 1 \] 3. Calculate \( 5(4) = 20 \): \[ -24 + 20 - 1 \] 4. Combine the terms: \[ -24 + 20 = -4 \] Then, \[ -4 - 1 = -5 \] Thus, the limit is: \[ \boxed{-5} \]

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