Introduction to rate of change calculator:
Here is an article which helps you as rate of change calculator.We will see here the formulas and some examples to calculate rate of change .In calculus we are using derivatives to find the rate of change of continuous functions.
The derivative ds/ dt stands for the rate of change of distance s wrt the time t.
In general ,if a quantity y varies wrt another quantity x satisfying some rule y=f(x),then dy/dx or f' (x) represent the rate of change of y wrt x
and f ' x at point x1 represent the rate of change at a specific point.
Further ,if two variables x and y are varying wrt another variable t, such that x =f(t) and y= g(t)
then
dy/dx = (dy/dt) /(dx/dt) provided dx/dt is not 0
Examples for Rate of Change Calculator
Example 1.Find the rate of change of the area of a circle with respect to radius r.How fast is the area changing wrt the radius when te radius is 2cm.
Answer:
We all know the formula for finding hte area of the circle.
as it is A= `pi *r^2`
So ,here we have to calculate the rate of change of A wrt to r.
so dA/dr =d( `pi * r^2`
which is 2 pi r
Now,we have to find How fast is the area changing wrt the radius when the radius is 2cm.
so r=2
so 4 pi
Answer: is 4 pi cm ^2/cm
I have recently faced lot of problem while learning how to solve equations with fractions, But thank to online resources of math which helped me to learn myself easily on net.
Problems on Rate of Change Calculator
1.Find the rate of change of the volume of a ball w r t its radius r. how fast is the volume changing w r t the radius when the radius is 2m?
Answer: 16 pi m 3 /m
2.The radius of the circle is increasing uniformly at the rate of 4cm per sec.
find the rate at which the area of the circle is increasing when the radius is 8cm.
Answer: (64 pi cm2 /s)
3.The volume of the cube is increasing at a rate of 7 cubic centimeters per sec.
How fast is the surface area increasing when the length of an edge is 1.2 centimeters.
Answer: 7/3 cm2/s at x=12
Here is an article which helps you as rate of change calculator.We will see here the formulas and some examples to calculate rate of change .In calculus we are using derivatives to find the rate of change of continuous functions.
The derivative ds/ dt stands for the rate of change of distance s wrt the time t.
In general ,if a quantity y varies wrt another quantity x satisfying some rule y=f(x),then dy/dx or f' (x) represent the rate of change of y wrt x
and f ' x at point x1 represent the rate of change at a specific point.
Further ,if two variables x and y are varying wrt another variable t, such that x =f(t) and y= g(t)
then
dy/dx = (dy/dt) /(dx/dt) provided dx/dt is not 0
Examples for Rate of Change Calculator
Example 1.Find the rate of change of the area of a circle with respect to radius r.How fast is the area changing wrt the radius when te radius is 2cm.
Answer:
We all know the formula for finding hte area of the circle.
as it is A= `pi *r^2`
So ,here we have to calculate the rate of change of A wrt to r.
so dA/dr =d( `pi * r^2`
which is 2 pi r
Now,we have to find How fast is the area changing wrt the radius when the radius is 2cm.
so r=2
so 4 pi
Answer: is 4 pi cm ^2/cm
I have recently faced lot of problem while learning how to solve equations with fractions, But thank to online resources of math which helped me to learn myself easily on net.
Problems on Rate of Change Calculator
1.Find the rate of change of the volume of a ball w r t its radius r. how fast is the volume changing w r t the radius when the radius is 2m?
Answer: 16 pi m 3 /m
2.The radius of the circle is increasing uniformly at the rate of 4cm per sec.
find the rate at which the area of the circle is increasing when the radius is 8cm.
Answer: (64 pi cm2 /s)
3.The volume of the cube is increasing at a rate of 7 cubic centimeters per sec.
How fast is the surface area increasing when the length of an edge is 1.2 centimeters.
Answer: 7/3 cm2/s at x=12
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