use-the-following-information-the-hyperbolic-sine-of-u-is-defined-as-sinh-ufrac12lefteu-e-uright-f-7

Question

Use the following information. The hyperbolic sine of $u$ is defined as $\sinh u=\frac{1}{2}\left(e^{u}-e^{-u}\right)$ Figure 27.30 shows the graph of $y=\sinh x$. The hyperbolic cosine of $u$ is defined as $\cosh u=\frac{1}{2}\left(e^{u}+e^{-u}\right)$ Figure 27.31 shows the graph of $y=\cosh x$. These functions are called hyperbolic functions since, if $x=\cosh u$ and $y=\sinh u, x$ and $y$ satisfy the equation of the hyperbola $x^{2}-y^{2}=1$. 
Show that $\frac{d}{d x} \sinh u=\cosh u \frac{d u}{d x}$ and $\frac{d}{d x} \cosh u=\sinh u \frac{d u}{d x}$
where $u$ is a function of $x$.

Cathy Wang · Accepted Answer

for this question That&#x27;s also still with the graph of the function y equals two into the bull X and no, first to get the graph off the function Y t ah, exchange a car. Why Tuesday won&#x27;t over to see to the parole fax And before this new function, we need to shrink. The graph of whyy goes to e x vertically by a fact off 1/2, which means each points off the new function this green function. Why value become half off the previous one off this brat function. So for the special point like here, the previous function must go across the points 01 one. Now the new function just drink. Whoa ha! Wish means the new function must go across a point they will want over, huh? So let&#x27;s get a new graph here. Yet the green line is a graph off. The one equals to walk over to eat it, throw off acts so similarly we can get why equals to one over to e to the post minus X uh, eat his home minus x just ah, in another direction here. So the blue lioce grapple. Wyche was toe t to the Po from minus X. And now we can use the graphic audition together our new function. Why you close to won&#x27;t Todt Home acts Claus. Well, t to 12 minus x. It actually s our up to function, Coach X. So you see, use a spool lying Teoh This red line, which means each off the point should add a little bit like this. A little bit A little bit a little Billy Billy. It will beat something like that. You will see Here&#x27;s ings issue off the green line, boo Like go across So point Ah, the robot over two. So this real I should go over Well, two plus one or two it was one this one point. So just like this? No. And there&#x27;s to function together. You get ah, I gather graph off the object function the coche excess function. So they say so question a The question be is used the definition to shoot kohsh Um minus X equal suu coach acts and the way expand by its definition iss Ah e x waas e minus x divided by two Oh, well, sorry. Let&#x27;s go back. Use a definition to expand the coach function we get to here&#x27;s e to pull off minus two Kloss e to the polls minus the minus X. Then you can get this minus minus ISS plus and the chance the water you were gods e x plus e to the post minus X and they actually the cold X.

Ankit Gupta · Answer

So in this question we have to find a local maximum and minimum values off GX and the X at which they occurred. So latest Andrada graph off X rays by eggs So we&#x27;re impressed by And then here, Chris X rays by ex dressed entered, then presume and six Soviet walked in the graph off X ray spot X latest find the minimum value So impressed second and then trace. So this gives us this option will press three. So here, the left monk Well, they would this on the right bump. They just put somewhere here I just entered. So this gives us the minimum value off at X is equal to 0.367 and the value of bias 0.69 So this can be round it off to 0.37 and 0.69 So value of G xs 0.69 id excess equipment 0.37 So this is the minimum value for maximum value as we can clearly see maximum value, absolute maximum will bear infinity, but let the scalp reducing our graph so well for a second and then pressed trace. Now, here will press four now the left round it s put somewhere here. So this is left bunk and let us portrayed bound some of it here. This dress enters so the maximum is coming off to be 3.60 on a maximum value of why is 109? But this is not a local maximum, because there is a greater value somewhere here, there for the absolute maximum will be infinity. On it will be at X rays but infinity. But when we calculate on this screen this is the local maximum value at X equal to 3.63 and the values 109.34 to it.

Joseph Lentino · Answer

Okay, so we&#x27;re doing some work with the natural base to talk about a hyperbolic co sign. Okay, so the hyperbolic co sign is defined as co sign Age of acts is equal to eat of the ax. Plus even the negative acts all divided by two. So we&#x27;re gonna use the graphs of the E to the X power divided by two and even the negative X divided by two to figure out exactly what this picture will look like. Okay, so let&#x27;s start by taking a look at, and I&#x27;ll do this in red. What does why equals one half e to the X look like? Well, everything is gonna be shifted down by by a scale of a half. So the graph will look something like this. If I graphed one half e to the negative X, I&#x27;m going to get a graph that will be just in the opposite direction. So look something like that Vac Toby. Reflections of one another. Well, if I take the two values and add them together, Okay. For example, if I took at negative 10 the red values really close to zero, But the green values wicked wicked heights close to infinity its way, way, way up there. So if I put the two graphs together and I use the some of these two graphs, the actual picture, we&#x27;ll end up looking like this. Half and a half adds upto one. It&#x27;s gonna get a graph that looks something like this when we add that you graphs together. Now what&#x27;s interesting about this is this graph is symmetrical to the Y axis, which makes it an even function. And by definition, the co sign of the opposite of a function will be equal to the co sign age of its function itself. Since it&#x27;s an even function, these will be equal to each other again because it&#x27;s even because it&#x27;s a reflection over the why.

Suman Saurav Thakur · Answer

you have a number 75 Invent. Oh, it is given there hyperbolic function off Sign that it&#x27;s signed You is beautifully power U minus u to the power minus you by two and bosh, you equal to UT power. You listen to the power minus you. So the question food if X equal to cost you and why would sign you? Throw that export Take X equals cost you Why I quit Sign you execute awesome life Abu sign you so indirectly We have X acquittal costing, which means eaters. But you listen to the power minus you. Divided by two And why I called toe get power you my power minus you. Would you like to? So x Esquire minus Why? Why squad will be b to the power you proceed to power minus you by two it was quite minus he to the power you edit of a minus you by two. Always good. So one by 41 by four will be common here. So it must be able to squared to the power to you. Plan C to the power minus two. You place to e to the power you into the power minus you This is okay for this heated power, Do you? Plus it to the power minus two U minus two it to the power you e to the power minus you. It will be 1/4 U to the power To you it is. Open the back. It it&#x27;s about to you present a power minus to you and u minus you zero So it will become too again it will become minus. It&#x27;ll power to U minus A to the power minus to you plus two. Because you should power bases the same human issue zero and e to the power zero equals to one. So this all these already could cancel out. So we will be having one by 42 plus two. Do you want by four into four equal to one, which means excess squad minus y squared equal to one. Thank you.

Suman Saurav Thakur · Answer

you have problems with 76 in which it is given that if x a quinto ceded power You president R minus you by the power u minus e to the power minus you and like will to you will buy. It is power. You manage that the power minus you. We need to show that at the Squire homes when it&#x27;s very cold. So let&#x27;s just do X squared minus y squared so u to the power you Plus he took part minus you into the power u minus C to the power minus. You was quite minus two by it was our u minus minus you old square. So let us right this u to the power you Plus it is part minus. You will square divide by two The power u minus heated minus you hold square minus four by you didn&#x27;t vote u minus u to the power of minors. You would square so we can see that the nominators are the same, so u to the power u minus C to the power my assholes Kirby Elsom should be good for you. Listen to the power minus you Hold Squire minus four. So let us open the bracket. It will be okay. One thing we can also do. You didn&#x27;t power you it for you. Plus to the power minus you. We&#x27;ll square minus four intuitive power. You we to the power minus you. As this is one each of our U minus e to the power minds. You all square now. We have a formula that a plus B squared minus 40 Be equal to a man. It&#x27;s a whole square it apart. Even minus two Power minus you. We&#x27;ll square It is our U minus C to the power minus you. Whole square saluted. Cancel out will be one So we can say that excess square minus y squared will be equal to one. Thanks so much.

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Use the following information. The hyperbolic sin…

Problem 55 Easy Difficulty

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus

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Basic Technical Mathematics with Calculus

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

Catherine R.

Anna Marie V.

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Allyn J. Washington, Richard S. Evans

Basic Technical Mathematics with Calculus