Brewer Newton
10/06/2023 · Elementary School

sea \( f(x)=3 x^{2}+x-1, \quad g(x)=2 x+3 \) \( \quad \) El \( \quad \lim _{x \rightarrow 3} f(g(x)) \quad \) es:

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Para encontrar el límite \( \lim_{x \rightarrow 3} f(g(x)) \), primero necesitamos calcular \( g(3) \) y luego usar ese resultado para encontrar \( f(g(3)) \). 1. Calculemos \( g(3) \): \[ g(x) = 2x + 3 \] Sustituyendo \( x = 3 \): \[ g(3) = 2(3) + 3 = 6 + 3 = 9 \] 2. Ahora, necesitamos calcular \( f(g(3)) = f(9) \): \[ f(x) = 3x^2 + x - 1 \] Sustituyendo \( x = 9 \): \[ f(9) = 3(9^2) + 9 - 1 \] Calculamos \( 9^2 \): \[ 9^2 = 81 \] Entonces: \[ f(9) = 3(81) + 9 - 1 = 243 + 9 - 1 = 243 + 8 = 251 \] Por lo tanto, el límite es: \[ \lim_{x \rightarrow 3} f(g(x)) = f(g(3)) = f(9) = 251 \] La respuesta final es: \[ \boxed{251} \]

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The limit \( \lim_{x \rightarrow 3} f(g(x)) \) is 251.
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