for-the-cantilever-column-in-exercise-32-of-section-104-find-xprimed-x-d-l-we-use-xprime-because-of-

Question

For the cantilever column in Exercise 32 of Section $10.4,$ find
$x^{\prime}(=d x / d L) .$ (We use $x^{\prime}$ because of the constant $d$ in the equation.)

Harry Evans · Accepted Answer

when we want to do that at restaurants from off code co sign h be of tea. Like the last question we&#x27;re just looking at. The formula off s over s squared, minus W scraped. And in this case, Toby is be So when we do it with B, we get s over s squared, minus B squared.

Harry Evans · Answer

when we want to do the last transform off Sign H off e t. We&#x27;re looking at the formula for a lot less transform When we do this as Don&#x27;t be you, Rosa squared minor, stubby spread with Don&#x27;t be being be so when we do it When we stop being we can be over s squared minus B squared.

Heather Zimmers · Answer

in this problem, we&#x27;re given the function f of X equals two X to the fourth and were asked to identify the power, the constant to graph it and to do some analysis, as was demonstrated in example, Number two in the book. So first of all, the power will be this exponents right here. So the power is for and the constant will be this number right here. So the constant is too for graphing. If you don&#x27;t know what the function is supposed to look like, You can always start by plotting some points. So I&#x27;m going to select some very simple X coordinates, substitute them into the function and find their Y coordinates. Negative too, would give us 32 negative One would give us 20012 3 32 And I&#x27;m going to plant those points. So let&#x27;s see what would be a good scale on the X axis, probably going by ones. And on the Y axis, it looks like those y values. They&#x27;re going to get pretty large. So how about if I put 16 here and 32 there and this is just a rough sketch, it doesn&#x27;t have to be perfect. So we have 00 We have one to that. Let&#x27;s say that&#x27;s right about there. We have 2 32 negative 2 32 So, depending on your scale, your graph may look more or less wide or narrow. This gives us a feel for the shape of the graph. It looks kind of like a parabola, although it&#x27;s not a parabola, because it&#x27;s not a quadratic function. But we do have symmetry across the Y axis. Let&#x27;s make a note of that. And any function that has symmetry across the Y axis is known as an even function. We can also verify that it&#x27;s an even function by doing our test, where we substitute in to the function the opposite of X. And if we do that, we have two times the opposite of X to the fourth, and we know that the opposite of X to the fourth is equivalent to X to the fourth. So this is equivalent to two extra the fourth and two extra. The fourth was our original function. So any time you do this test and you discover that F of the opposite of X is equal to F of X You know that you haven&#x27;t even function. If you discover that they&#x27;re opposites, then you know you have an odd function. Okay, For the rest of the analysis, it&#x27;s always good to see what the domain is. Notice that X could be any real number. You can have positive negative zero. You could even have irrational numbers and raise them to the forth and multiply that by two. And you can see by the graph we go through all X values. So we&#x27;re gonna say all real numbers. You can also see from the graph that the range the set of why values for the function or the set of outputs They&#x27;ve got to be zero or greater because any real number that you raised to the fourth power is going to be zero or positive. So we&#x27;re going to say the interval from zero to infinity, including zero. This is a continuous function because we can draw the whole thing without lifting a pencil. It doesn&#x27;t have brakes or gaps or holes in it. It also decreases for a while and then it increases. It&#x27;s decreasing where you see it going down as it moves from left to right when it&#x27;s going down and that would be on the first half of the graph from negative infinity to zero and then it increases. That&#x27;s where it&#x27;s going up. As you move from left to right. It&#x27;s going up and that&#x27;s happening from zero to infinity now, since you don&#x27;t have any points below height of zero, we could say that it&#x27;s bounded below. We could say it has a local minimum since it has the lowest point. We&#x27;ll call that a minimum and that is the 0.0 And ah, this particular graft does not have any Assen totes and the last thing we want to talk about is what&#x27;s happening as X goes toward infinity. So the way we describe that, as we say, the limit of the function as X goes toward infinity, that means what&#x27;s the end behavior of the function? What are the Y values doing as the X values get greater and we can see if we look at the graph that the Y values air getting greater as the X values get greater. So the Y values are also heading toward infinity. And then what are the Y values doing as the X values had toward negative infinity on the left half of the graft. What&#x27;s the limit of the function while it&#x27;s also heading up on both sides? So it&#x27;s heading up toward infinity, whether you are heading toward the left or heading toward the right, and that pretty much sums up our function and all of its characteristics, so that is the end of the video.

Tani Iqbal · Answer

So we&#x27;re told off of X is equal to 32 we also know what&#x27;s given to us is f of X is due to the X. So he said to to the x equal. So 32 we know that 32 is the same thing as to to the something power. If you forget, make a little factor tree. If I pull out four and eight four gets me to in Tube eight gets me two and 44 gets me to. And two I have 123452 So you get to to the X is equal to to do the five. Our bases are the same, so you can set the exponents equal to each other and get X is equal to five, and that is your answer.

Robert Daugherty · Answer

Section six That three. Problem number 29. We&#x27;re solving a differential equation so I can write this as d y is equal to x squared e to the four x the X I can integrate those sides of this equation and to solve her Why Why is going to be the integral of X squared e to the four x the ex Now I will integrate my parts. You is equal to X squared. Therefore d&#x27;you is equal to two ex The ex Devi is equal to eat to the four X. Therefore, V is equal to 1/4 e to the fore x So this interval becomes X squared e to the four x d x is equal to u v. So that is 1/4 x squared e to the four acts minus the integral of the d you. So this is gonna be minus 1/2 and this becomes X E to the four x d. X. Now what I need to do is once again integrate by parts on this particular into grand. So here I will let you equal X, the U. S equipped to D X, and then the same thing. Devi Izzy to the four x the is equal to 1/4 e to the four x. So when I do that, I get that this integral X squared e to the four. X d x is equal to 14 x squared e to the four X minus 1/2 Now on to figure out what is UV So you ve is, um X over four e to the four x minus VD you So this is minus 1/4 E to the four x the ex. So let me just copy this down on the next page. So that was integral X squared E to the four X. The ex was equal to what? That I have 1/4 x squared e to the four X. And so let&#x27;s just distribute then. So if I look at this first term you see right here, that&#x27;s gonna be what, um, minus 1/8 x E to the four x so minus one eight x e to the four X And then if you look at the next term, that&#x27;s gonna be a, um when you integrate either the four ex, um, that&#x27;s gonna remember integrating eat of four X is going to give me 1/4 beat of the four X. So So that&#x27;s gonna be 1/16 and 1 32nd So plus 1 32nd So plus one 32nd you to the four x plus. See? Okay, and that should be it. We can make this a little simpler if we factor out what we have in common. So let&#x27;s just see. I can factor out, um, and eat of the four X right? So and I could also write this in terms of, um if I factor out, I could always also write things in terms of 30 seconds so I could write this as what I ate over 32 x squared E to the four x minus, um, for over 32 XY to the four X plus one over 30 to you to the four acts plus C. And then I could factor out one 30 seconds you to the four X, and I&#x27;m left with eight X squared plus four x plus one plus c. So we were perfectly good with an answer. This is a perfectly good answer right here, and this is just factoring out a little bit further, but you should get to

Problem

Solve the given problems. A helicopter takes off …

Problem 49 Easy Difficulty

For the cantilever column in Exercise 32 of Section $10.4,$ find
$x^{\prime}(=d x / d L) .$ (We use $x^{\prime}$ because of the constant $d$ in the equation.)

Answer

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

Grace H.

Catherine R.

Kayleah T.

Kristen K.

Precalculus Review - Intro

Functions on the Real Line - Overview

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Basic Technical Mathematics with Calculus

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Allyn J. Washington, Richard S. EvansBasic Technical Mathematics with Calculus

Grace H.

Catherine R.

Kayleah T.

Kristen K.

Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus