Question
Dada la función \( g(x)=\left(-4 x^{\wedge} 2+3 x+1\right)^{\wedge} 2, \quad * \) calcular el límite cuando \( x \) se aproxima a -1
Ask by Hodgson Washington. in Mexico
Oct 29,2024
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Tutor-Verified Answer
Answer
El límite de \( g(x) \) cuando \( x \) se aproxima a -1 es 36.
Solution
Calculate the limit \( \lim_{x\rightarrow -1} (-4x^2 + 3x + 1)^2 \).
Evaluate the limit by following steps:
- step0: Evaluate the limit:
\(\lim _{x\rightarrow -1}\left(\left(-4x^{2}+3x+1\right)^{2}\right)\)
- step1: Rewrite the expression:
\(\left(\lim _{x\rightarrow -1}\left(-4x^{2}+3x+1\right)\right)^{2}\)
- step2: Calculate:
\(\left(-6\right)^{2}\)
- step3: Determine the sign:
\(6^{2}\)
- step4: Evaluate the power:
\(36\)
El límite de la función \( g(x) = (-4x^2 + 3x + 1)^2 \) cuando \( x \) se aproxima a -1 es igual a 36.
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