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Mathematics

2 answers:

Papessa [141]3 years ago

4 0

For the equation, the rate of change would be four.
Now looking at the graph, look at each point of the line that hits perfectly on a grid. Count up four, over two. The rate of change for the graph would be 4/2, or 2. Hope this helps!

ankoles [38]3 years ago

4 0

Hi there!

Graph:
The rate of change is 2.

If we take the points (3,2) and (1, -2) and use slope triangles to find the slope, 4 ÷ 2 = 2, so the slope is 2.

Function:
The rate of change is 4.
The rage of change in a function in slope intercept form is always the number before x.

Hope this helps!

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Answer:

The sequence converges to infinity.

Step-by-step explanation:

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

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