1.
Which is the graph of the exponential function y = 0.5(0.5)x?

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Ответ:

daniel1480

04.02.2023

Mathematics

The answer is " The sequence converges to infinity. "

Step-by-step explanation:

Given:

$\to a_n=\frac{n^3-n}{n^2+5n}$

$\lim_{n \to \infty} a_n= \lim_{n \to \infty} \frac{n^3-n}{n^2+5n}$

$= \lim_{n \to \infty} \frac{n(n^2-1)}{n(n+5)}\\\\= \lim_{n \to \infty} \frac{(n^2-1)}{(n+5)}\\\\= \lim_{n \to \infty} \frac{n(n-\frac{1}{n})}{n(1+\frac{5}{n})}\\\\= \lim_{n \to \infty} \frac{(n-\frac{1}{n})}{(1+\frac{5}{n})}\\\\$

Denominator $= \lim_{n \to \infty} 1+\frac{5}{n}=1+\lim_{n\to \infty} \frac{5}{n}=1+0=1$

Numerator $=\lim_{n\to \infty}n-\frac{1}{n}=\infty$

$\therefore\\\\\lim_{n\to \infty}a_n=\frac{\infty}{1} =\infty$

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1. Which is the graph of the exponential function y = 0.5(0.5)x?