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Graph the function by hand, not by plotting point…

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Problem 19 Easy Difficulty

Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions given in Section 1.2, and then applying the appropriate transformations.

$ y = \sin (\frac{1}{2} x) $


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Calculus: Early Transcendentals

Chapter 1

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Multivariate Functions - Intro

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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Partial Derivatives - Overview

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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Watch More Solved Questions in Chapter 1

Problem 1
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Problem 7
Problem 8
Problem 9
Problem 10
Problem 11
Problem 12
Problem 13
Problem 14
Problem 15
Problem 16
Problem 17
Problem 18
Problem 19
Problem 20
Problem 21
Problem 22
Problem 23
Problem 24
Problem 25
Problem 26
Problem 27
Problem 28
Problem 29
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Problem 31
Problem 32
Problem 33
Problem 34
Problem 35
Problem 36
Problem 37
Problem 38
Problem 39
Problem 40
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Problem 46
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Problem 48
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Problem 51
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Problem 53
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Problem 55
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Video Transcript

to graph this function, we're going to start by looking at the graph of the standard function y equals sign of X, so we know that it has a period of two pi. That's the with that one cycle, and we knew it goes up to a height of one and down to a height of negative one. So it looks roughly like this. Now what happens to it if we multiply the X by 1/2 that represents a horizontal stretch, so it's going to be two times as wide. So we say horizontal stretch by a factor of two that changes the period. The width of one cycle is now going to be four pi instead of two pi. So if you want to draw it out that far, we can still goes up to a height of one and down to a height of negative one. That didn't change. So now we have the graph that is stretched out wider, like so

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Video Thumbnail

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