Answer:
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Answer:
∫((cos(x)*dx)/(√(1+sin(x)))) = 2√(1 + sin(x)) + c.
Step-by-step explanation:
In order to solve this question, it is important to notice that the derivative of the expression (1 + sin(x)) is present in the numerator, which is cos(x). This means that the question can be solved using the u-substitution method.
Let u = 1 + sin(x).
This means du/dx = cos(x). This implies dx = du/cos(x).
Substitute u = 1 + sin(x) and dx = du/cos(x) in the integral.
∫((cos(x)*dx)/(√(1+sin(x)))) = ∫((cos(x)*du)/(cos(x)*√(u))) = ∫((du)/(√(u)))
= ∫(u^(-1/2) * du). Integrating:
(u^(-1/2+1))/(-1/2+1) + c = (u^(1/2))/(1/2) + c = 2u^(1/2) + c = 2√u + c.
Put u = 1 + sin(x). Therefore, 2√(1 + sin(x)) + c. Therefore:
∫((cos(x)*dx)/(√(1+sin(x)))) = 2√(1 + sin(x)) + c!!!
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Answer:
Now we can find the second central moment with this formula:
And replacing we got:
And the variance is given by:
And replacing we got:
And finally the deviation would be:
Step-by-step explanation:
We can define the random variable of interest X as the return from a stock and we know the following conditions:
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represent the result if we have a recession
We want to find the standard deviation for the returns on the stock. We need to begin finding the mean with this formula:
And replacing the data given we got:
Now we can find the second central moment with this formula:
And replacing we got:
And the variance is given by:
And replacing we got:
And finally the deviation would be: