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:
The value of is
Explanation:
The function is given by
The function is given by
To determine the value of , let us first substitute the value of
.
Thus, we get,
Now, substituting for in the function
, we get,
Simplifying, the expression, we get,
Multiplying the term within the bracket, we have,
Thus, the value of is
Hence, the value of represents the total amount of money that Barrett earns for working x hours.