what does it mean to linearize a graph Subscribed 2 7K 207K views 7 years ago Physics Background Material This lesson describes the process of linearizing graphs Linearizing is a method of recognizing one of three shapes of
Linearizing a graph allows you to apply various statistical tools such as regression analysis with confidence By transforming the data into a linear form you can make more accurate predictions identify significant trends and uncover hidden patterns Describe the linear approximation to a function at a point Write the linearization of a given function Draw a graph that illustrates the use of differentials to approximate the change in a quantity Calculate the relative error and percentage error in using a differential approximation
what does it mean to linearize a graph
what does it mean to linearize a graph
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In mathematics linearization is finding the linear approximation to a function at a given point The linear approximation of a function is the first order Taylor expansion around the point of interest This demo shows visually how linearizing a function and using known points as an anchor will allow you to easily find a very close approximation of the true value Linearization is useful when you do not have a calculator Set the function you want to linearize equal to f x T is the target point This is the value you want to approximate
Key Takeaways Linearizing a graph in Excel is important for easier interpretation of trends and making predictions based on data Understanding the data set and inputting it correctly into Excel is crucial for creating an accurate initial graph Having found a good linear fit to tsq the transformed data we can now back transform the equation for the line to get the equation for time Since tsq time 2 and tsq 0 2 height we can substitute to get time 2 0 2 height or time sqrt 0 2 height The resulting graph looks like this
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Fundamentally a local linearization approximates one function near a point based on the information you can get from its derivative s at that point In the case of functions with a two variable input and a scalar i e non vector output this can be 1 1 2 Procedure for Linearization The steps are as follows Rearrange the equation to get one variable or a function of it on the left side of the equation this becomes your y variable Regroup the right side of the equation to create a term containing the other variable or some function of it
A linearization of this graph is an order of the individual steps such that all their dependencies are executed before each step itself For this example the graph itself is already linear and can be executed as is Things get a bit more complicated if the graph contains branches Linearization In single variable calculus an important use of the tangent line is to approximate the value of a differentiable function Near the point x0 x 0 the tangent line to the graph of f f at x0 x 0 is close to the graph of f
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what does it mean to linearize a graph - Having found a good linear fit to tsq the transformed data we can now back transform the equation for the line to get the equation for time Since tsq time 2 and tsq 0 2 height we can substitute to get time 2 0 2 height or time sqrt 0 2 height The resulting graph looks like this