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:
Answer:
0.67 cm/s
Step-by-step explanation:
The area of a square is given by :
....(1)
Where
x is the side of a square
Differentiating equation (1) wrt t.
When A = 81cm², the side of the square, x = 9 cm
Put all the values,
So, the length of the side of a square is changing at the rate of 0.67 cm/s.
Answer:
Step-by-step explanation:
Given
Required:
Simplify
We start by opening the bracket
Collect Like Terms
Hence, the equivalent expression is