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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Step-by-step Solution
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:
\[
\boxed{251}
\]
Quick Answer
The limit \( \lim_{x \rightarrow 3} f(g(x)) \) is 251.
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