use the appropriate limit laws and theorems to determine the limit of the sequence.\n(b_{n}=e^{9…

use the appropriate limit laws and theorems to determine the limit of the sequence.\n(b_{n}=e^{9 - n^{2}})\n(give an exact answer. use symbolic notation and fractions where needed. enter dne if the sequence diverges.)\n(lim_{n\rightarrowinfty}b_{n}=)

use the appropriate limit laws and theorems to determine the limit of the sequence.\n(b_{n}=e^{9 - n^{2}})\n(give an exact answer. use symbolic notation and fractions where needed. enter dne if the sequence diverges.)\n(lim_{n\rightarrowinfty}b_{n}=)

Answer

Explicación:

Paso 1: Analizar el exponente

Consideramos el exponente $9 - n^{2}$. Cuando $n\to\infty$, $9 - n^{2}\to-\infty$.

Paso 2: Usar la propiedad del exponencial

Sabemos que $\lim_{x\to-\infty}e^{x}=0$. Aquí, si $x = 9 - n^{2}$ y $n\to\infty$, entonces $\lim_{n\to\infty}e^{9 - n^{2}}=0$.

Respuesta:

$0$