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What is the difference between mean value theorem of integration and Mean Value Theorem of differentiation?
The mean value theorem for differentiation guarantees the existing of a number c in an interval (a,b) where a function f is continuous such that the derivative at c (the instantiuous rate of change at c) equals the average rate of change over that interval. mean value theorem of integration guarantees the existing of a number c in an interval (a,b)where a function f is continuous such that the (value of the function at c) multiplied by the length of the interval (b-a) equals the value of a the definite integral from a to b. In other words, it guarantees the existing of a rectangle (whose base is the length of the interval b-a that has exactly the same area of the region under the graph of the function f (betweeen a and b).
How does average change help find instant rate of change in math?
This is done with a process of limits. Average rate of change is, for example, (change of y) / (change of x). If you make "change of x" smaller and smaller, in theory (with certain assumptions, a bit too technical to mention here), you get closer and closer to the instant rate of change. In the "limit", when "change of x" approaches zero, you get the true instantaneous rate of change.
What happens to R-R interval after exercise?
During exercise an increase in heart rate corresponds to a shortening of the cardiac cycle (RR interval decreases). Most of this shortening occurs in the TP interval. The QT interval also shortens, but only slightly. then the interval shortens as the heart rate increases.
How does the slope differ from average rate of change?
They are the same for a straight line but for any curve, the slope will change from point to point whereas the average rate of change (between two points) will remain the same.
What is a constant rate?
a non-stop rate * * * * * No it is not. A non-stop rate can be faster and slower and faster and faster still etc. That is NOT a constant rate, A constant rate means the same amount for any unit of time in the whole time interval. The rate must not change at all from start to finish.
