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It is the rate of change at one given moment, and it is the same as the value of the derivative at a particular point. The point may be thought of as that given moment. When we talk about functions, the instantaneous rate of change at a point is the same as the slope, m, of the tangent line.. Sometimes we think of it as the slope of the curve. The best way to understand this is with the difference quotient and limits. The difference quotient is the average rate of change of y with respect to x. If we then look at the difference quotient and we let delta x ->0, this will be the instantaneous rate of change. In other words, the time interval gets smaller and smaller. Difference quotient is delta y/ delta x where delta represents the change.
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What is the difference between derivative and differenciation?
derivative means rate of change of one variable w.r.t one variable while in differentition rate of change of one variable w.r.t more than one variables.
What does the slope of the curve on a velocity time graph represent?
The rate of Change in acceleration.
What is calculus and what does it have to do with?
Calculus is a branch of mathematics which came from the thoughts of many different individuals. For example, the Greek scholar Archimedes (287-212 B.C.) calculated the areas and volumes of complex shapes. Isaac Newton further developed the notion of calculus. There are two branches of calculus which are: differential calculus and integral calculus. The former seeks to describe the magnitude of the instantaneous rate of change of a graph, this is called the derivative. For example: the derivative of a position vs. time graph is a velocity vs. time graph, this is because the rate of change of position is velocity. The latter seeks to describe the area covered by a graph and is called the integral. For example: the integral of a velocity vs. time graph is the total displacement. Calculus is useful because the world is rarely static; it is a dynamic and complex place. Calculus is used to model real-world situations, or to extrapolate the change of variables.
What does the gradient of a graph tell you?
It tells you the rate of change of the variable mapped along the vertical axis relative to the change in the variable mapped along the horizontal axis.
Are mortgage payoff calculators accurate?
Mortgage payoff calculators are accurate, however they are only accurate if your morgagte doesn't change in the future. For example, if you change your rate and refinance, a prior calculation might not be accurate.
The rate of change in position at a given point in time?
Ah, honey, you're talking about velocity! Velocity is the rate of change in position at a specific point in time. It's like speed dating for math - how fast an object is moving at any given moment. So next time someone asks about the rate of change in position, you can confidently say, "Oh, that's just velocity, darling."
What is application of differentiator?
Finding the rate of change - in particular, the instantaneous rate of change.
What is the rate of change in a position at a given point in time?
The rate of change in position at a given point in time is instantaneous speed, instantaneous velocity.
What is the rate of change in position in a given point of time?
The rate of change in position at a given point in time is instantaneous speed, instantaneous velocity.
What is The rate in change of position at a given point in time?
The rate of change in position at a given point in time is instantaneous speed, instantaneous velocity.
What is the difference between a slope and rate of change?
Depends. Slope of tangent = instantaneous rate of change. Slope of secant = average rate of change.
At a given moment in time instantaneous speed can be though of as the magnitude of instantaneous of what?
At a given moment in time, instantaneous speed can be thought of as the magnitude of the instantaneous velocity of an object. Instantaneous velocity is the rate of change of an object's position at that specific moment in time.
Is the rate at which an object changes velocity?
No, velocity is the instantaneous speed of an object, the rate of change would be the acceleration of the object.
What is the rate of change of position at a specific point in time?
The rate of change of position is the velocity. The velocity at a specific point in time is called the instantaneous velocity.
What's the difference between instantaneous velocity and instantaneous acceleration?
Instantaneous velocity represents the rate of change of an object's position at a specific moment in time, while instantaneous acceleration represents the rate of change of an object's velocity at a specific moment in time. In other words, velocity measures how fast an object is moving, while acceleration measures how fast the object's velocity is changing.
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 is instentaneous acceleration?
Instantaneous acceleration is the rate of change of velocity at a specific moment in time. It indicates how quickly the velocity of an object is changing at that instant. It is typically calculated as the derivative of velocity with respect to time.
