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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 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.
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.
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.
