Numerical analysis | Differential calculus
In single-variable calculus, the difference quotient is usually the name for the expression which when taken to the limit as h approaches 0 gives the derivative of the function f. The name of the expression stems from the fact that it is the quotient of the difference of values of the function by the difference of the corresponding values of its argument (the latter is (x + h) - x = h in this case). The difference quotient is a measure of the average rate of change of the function over an interval (in this case, an interval of length h). The limit of the difference quotient (i.e., the derivative) is thus the instantaneous rate of change. By a slight change in notation (and viewpoint), for an interval [a, b], the difference quotient is called the mean (or average) value of the derivative of f over the interval [a, b]. This name is justified by the mean value theorem, which states that for a differentiable function f, its derivative f′ reaches its mean value at some point in the interval. Geometrically, this difference quotient measures the slope of the secant line passing through the points with coordinates (a, f(a)) and (b, f(b)). Difference quotients are used as approximations in numerical differentiation, but they have also been subject of criticism in this application. Difference quotients may also find relevance in applications involving Time discretization, where the width of the time step is used for the value of h. The difference quotient is sometimes also called the Newton quotient (after Isaac Newton) or Fermat's difference quotient (after Pierre de Fermat). (Wikipedia).
What is a difference quotient? How to find a difference quotient. Deriving it from the rise over run formula.
From playlist Calculus
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We present a few examples of calculating the difference quotient. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist PreCalculus
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👉 Learn how to evaluate the limit of a function using the difference quotient formula. The difference quotient is a measure of the average rate of change of the function over an interval, h. The limit of the difference quotient gives the derivative of the function. The difference quotient
From playlist Evaluate the Limit (PC)
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From playlist Evaluate the Limit..........Help!
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👉 Learn how to evaluate the limit of a function using the difference quotient formula. The difference quotient is a measure of the average rate of change of the function over an interval, h. The limit of the difference quotient gives the derivative of the function. The difference quotient
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Learn how to simplify the difference quotient in this video math tutorial by Mario's Math Tutoring. We go through 3 examples: one involving fractions, another square roots, and the third one is a quadratic function. We also discuss how if you take the difference quotient one step further
From playlist Difference Quotient & Derivatives
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Thanks to all of you who support me on Patreon. You da real mvps! $1 per month helps!! :) https://www.patreon.com/patrickjmt !! The Difference Quotient - Example 1. In this video, I give the formula for the difference quotient (aka, the subtraction fraction) and do a couple examples of
From playlist All Videos - Part 6
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👉 Learn how to evaluate the limit of a function using the difference quotient formula. The difference quotient is a measure of the average rate of change of the function over an interval, h. The limit of the difference quotient gives the derivative of the function. The difference quotient
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From playlist What is a Manifold?
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👉 Learn how to evaluate the limit of a function using the difference quotient formula. The difference quotient is a measure of the average rate of change of the function over an interval, h. The limit of the difference quotient gives the derivative of the function. The difference quotient
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