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A(h) =2 (pi) root[1+(h+1)^2] ... then ?Simon Bridge said:Don't you have an expression for A(h)?
I don't know what is V(h), I try to assume it as V(h)= A(h)[h] = 2 (pi) root[1+(h+1)^2] h for small interval of h, but I don't know if it is correct.Simon Bridge said:Do you have V(h) then?
That looks like the circumference of the circular surface, not the area.Clara Chung said:A(h) =2 (pi) root[1+(h+1)^2] ... then ?
A(h) = pi(1+(h+1)^2)SammyS said:That looks like the circumference of the circular surface, not the area.
That looks better.See what Simon said:Clara Chung said:A(h) = pi(1+(h+1)^2)
=pi (2+2h+h^2)
dA(h) / dt = pi(2h+2)dh/dt
=24/5
thanks
Notice: It's pretty easy to display your image directly in a post:Simon Bridge said:(BTW: very few people will trouble to read images.)
You should start a new thread for this.Clara Chung said:Thank you for the advice from you both. Can you also teach me how to show that "1-t^2/2 <=cost <=1 for 0<=t<=1 "
The rate of change problem in differentiation is a mathematical concept that involves finding the rate at which one quantity changes with respect to another quantity. It is often used to analyze the behavior of a function and to determine the slope of a curve at a specific point.
The rate of change can be found using the derivative, which is a mathematical tool used in differentiation. To find the derivative of a function, you need to take the limit of the function as the change in the independent variable approaches 0. This will give you the slope of the tangent line at a specific point, which is the rate of change.
The rate of change is important in science because it allows us to understand how a system or process is changing over time. By analyzing the rate of change, we can make predictions about the future behavior of a system and make informed decisions about how to control or manipulate it.
The rate of change problem has many real-world applications in fields such as physics, economics, and engineering. For example, it can be used to calculate the speed of an object, the growth rate of a population, or the rate of reaction in a chemical reaction.
There are several techniques for solving rate of change problems, including the power rule, product rule, quotient rule, and chain rule. These rules help you find the derivative of more complex functions by breaking them down into simpler parts. Additionally, graphing and using numerical methods can also be helpful in solving rate of change problems.