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Graph the given functions on the same screen. How are these graphs related?
$ y = \tan x $ , $ \frac{-\pi}{2} < x < \frac{\pi}{2} $ ; $ \tan^{-1} x $ ; $ y = x $
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01:08
Jeffrey Payo
Calculus 1 / AB
Calculus 2 / BC
Calculus 3
Chapter 1
Functions and Models
Section 5
Inverse Functions and Logarithms
Functions
Integration Techniques
Partial Derivatives
Functions of Several Variables
Campbell University
Harvey Mudd College
Baylor University
University of Michigan - Ann Arbor
Lectures
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A multivariate function is a function whose value depends on several variables. In contrast, a univariate function is a function whose value depends on only one variable. A multivariate function is also called a multivariate expression, a multivariate polynomial, a multivariate series, or a multivariate function of several variables.
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In calculus, partial derivatives are derivatives of a function with respect to one or more of its arguments, where the other arguments are treated as constants. Partial derivatives contrast with total derivatives, which are derivatives of the total function with respect to all of its arguments.
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okay we're using or graphing calculators were going to go to the y equals menu, and we want to graph y equals tangent of X as well as y equals inverse tangent of X as well as y equals X. Now let's go to mode and make sure our calculator is set to radiance. And if not, you want to change it to radiance. And now let's go toe window. And we want our X values to go from negative pi over to two pi over to so weaken. Type that in. Actually use your pie button for accuracy there to have negative pi over two pi over two and then for the y values. We could have different ideas for this. I'm just going to go with, say, negative 5 to 5 and if I don't like it, I can change it. So let's look at the graph. Okay, so if you press trace, you'll be able to tell which color is for which graph. So the blue one is for the tangent graph. The red one is the inverse tangent graph, and the black one is the line y equals X. So what we noticed is that the tangent and the inverse do look like reflections of each other across the line Y equals X, as in verses should.
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