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Answer:
knowing your personal values will help you to know when the other individuals values do not align with yours.
The <em>average rate of change</em> of the function y = cos(2x) over the interval (0, π/2) is
The <em>average rate of change</em> over a given interval is defined thus :
- Where a and b are the interval values
<u>At a = </u><u>0</u><u> </u><u>:</u><u> </u>
- f(0) = cos(2(0)) = Cos 0 = 1
<u>At b = π/2</u> :
- f(π/2) = cos(2(π/2)) = Cos π = - 1
Hence,
Therefore, the <em>average rate of change</em> over the interval is
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The indefinite integral expressed as an infinite series is;
<h3>How to find indefinite integral?</h3>
We will first have to look for the Maclaurin series of arctan(x).
We'll recall that from online tables of integral, this Maclaurin series of arctan(x) will have the general formula;
When we apply that general Maclaurin series of arctan(x) to our question of arctan(x²), we have the expression as;
⇒
We now integrate the expression that we got above in the following manner to get;
⇒
Thus, that expression gives us the indefinite integral of arctan(x²) as an infinite series.
Read more about the indefinite integral at; brainly.com/question/12231722