What is the rate of change between the interval of x = 0 and x = π/2?

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The rate of change between two points in mathematics is commonly represented by the concept of the slope or derivative, especially when dealing with a function. When we examine the interval from x = 0 to x = π/2, we can calculate the rate of change of a specific function, such as f(x) = sin(x), f(x) = cos(x), or any other relevant function of your choice.

To find the rate of change, we’ll use the formula:

Rate of Change = (f(b) - f(a)) / (b - a)

In our case, let:

  • a = 0
  • b = π/2

Now, if we take the sine function as an example:

f(0) = sin(0) = 0
f(π/2) = sin(π/2) = 1

Substituting these values into our rate of change formula, we get:

Rate of Change = (f(π/2) - f(0)) / (π/2 - 0) = (1 - 0) / (π/2) = 2/π

Therefore, the rate of change of the function f(x) = sin(x) from x = 0 to x = π/2 is 2/π.

Similarly, you can calculate the rate of change for other functions by substituting their respective values into this formula. Understanding the rate of change in a particular interval helps in analyzing how functions behave over that span, providing insights into their overall performance and trends.

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