Determine if the following table represents a quadratic function.
1 answer:
Answer:
<em>The options are not visible enough (See Explanation)</em>
Step-by-step explanation:
Given
x:- 1 || 2 || 3 || 4 || 5
y:- 13 || 22 || 37 || 58 || 85
Required
Determine if the function is quadratic
Calculate the difference between the values of y
<em>The resulting difference are: 9 || 15 || 21 || 27</em>
Next; Calculate the difference between the difference of values of y
<em>The resulting difference are: 6 || 6 || 6</em>
<em>For the function to be quadratic, the above difference must be the same and since they are the same (6), then the function represents a quadratic function.</em>
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Answer:
We want to find:
Here we can use Stirling's approximation, which says that for large values of n, we get:
Because here we are taking the limit when n tends to infinity, we can use this approximation.
Then we get.
Now we can just simplify this, so we get:
And we can rewrite it as:
The important part here is the exponent, as n tends to infinite, the exponent tends to zero.
Thus: