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Problem

Starting with the graph of $ y = e^x $, write the…

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Problem 16 Medium Difficulty

Make a rough sketch of the graph of the function. Do not use a calculator. Just use the graphs given in Figures 3 and 13 and, if necessary, the transformations of Section 1.3.

$ y = 2 (1 - e^x) $


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Jeffrey Payo

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Calculus: Early Transcendentals

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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
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
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
Problem 30
Problem 31
Problem 32
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Problem 34
Problem 35
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Problem 37
Problem 38

Video Transcript

here. We're going to make a rough sketch emphasis on rough. And the point of that is to show that we understand the basic shape of the graph and we, But we understand the transformations it went through, and I'm going to start by changing how this function looks just a little bit. I'm going to distribute the to So Y equals two minus to each of the X, And then I'm going to rearrange the order of the terms. Why equals negative to e to the X Plus two. If I have it written that way, it's going to help me with the transformations. Okay, so I'm going to start with the basic function. Why equals each of the X? That's your basic exponential growth. And then what I'm going to do is multiply it by two. Multiplying it by two is going to stretch it twice as tall. So instead of having a Y intercept at one, it's going to have a Y intercepted two, and every point is going to be twice as high as it previously. Waas. Okay, the next thing I'm going to do is notice that it's multiplied by a negative, and that's going to reflect it across the X axis. So now it's going to be down here, Okay. And then the last thing I noticed is that, too is added. And when you add two to a function, you're going to shift the whole thing up to now. Where was the horizontal Assen tote All along the way it was at y equals zero. It was still at y equals zero, and it was still it Y equals zero. But now that I'm going to shift the whole graf up to the horizontal Assen Tote is going to be at y equals two. That's kind of our boundary line for this graph. So when we shifted up, the Y intercept is now going to be here at 00 and we're gonna follow that boundary line

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