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Think and AnswerGive an example of a nonlinear two-point boundary-value problem:...

Question

Think and AnswerGive an example of a nonlinear two-point boundary-value problem:

Think and Answer Give an example of a nonlinear two-point boundary-value problem:



Answers

What is a system of nonlinear equations? Provide an example with your description.

Question is asking that what is unknown linear system of the situation. So and only new system of education is defined as a system off decoration where it contains more than one creation toe, or more than two equations with two or more variables. And from these decorations, at least one decoration should be known lenient. So this is the system of known linear equations. Now, let's see example off known linear system arbitrations. So the first equation, which we can write for this system, is access choir plus wise wire is it was to fight. And the second equation, which we will write for this system, is active Squire minus wise, while because to 30 now ed board the equations equation number to any question number one. So from there we can rewrite it edge to access quality close to 18 and access pretty close to nine and X is equals two plus miners. Three. These are to be news for these two equations. So now we need to find out the value why respect toe you back. So put X equals two plus three in equation number two. Then they will have the value. Why in misery and the same for tax. It was toe minus tree. Then also, the value will be imaginary for Why? So this system of equations is known linear, but don't have any real solution. So this is the answer of this question.

Well, I'm gonna be explaining what a system of nonlinear equations is and giving you some examples that you can kind of look at to be able to identify those. So ah, system of to nonlinear equations has two separate variables. So typically, we would be solving for X, or why on and has one equation, um, that you would usually use to find, um, variable on the other by substituted. So the sets have ordered pairs that satisfy the equations in the system so the nonlinear systems can have intersection points on a graph due to the equations and the system. It could be a graph that shows the circles ellipse sees things like that, and non linear systems can be self by, substituting each other in and out to try and find one variable in terms of the other. So maybe you're finding X in terms of why or why in terms of X and then you're using addition then and the addition method to be able to solve. So an example of this could be, let's just say like X squared equals maybe six Y minus 10. And then you could have potentially four X minus six y equals two. So that's one example of nonlinear systems of equations. Um, but the first example here that I'm gonna give you it's not in a format of eight times x plus b times. Why? Will see. So that's typically what we look at for the form for these nonlinear equations was go right. This here as a visual, so those aren't for mounted the exact same, but they are nonlinear systems that could be solved by substituting in. So basically what you do is you try and eliminate the six. Why, um and then solve For what? Exit B in terms of why and then another example you could use, which I'm just gonna show what it would look like if it is in that format, you could use X squared minus two y squared equals six on. Then you could have maybe two X squared minus three y squared equals 12. Um, and again here, you could maybe multiply out to get rid of the two x squared. But in this system, the separate example um, you see the equations both have squared powers for your variables of accent. Why? So you would have toe solve for the square roots of those

So your question is, what is the system off normal in your equation? So begins about the system off. No linear equation is a pair of the question with at least one off to equation. Not having a form off X place be right is equal to see are why is he will toe mx plus C, right? For an example, we can write. Ah, let our first equation is X squared plus y spreads It is a golden nine and the other one is wise equal due to explore street. So this is your system off known in immigration, right? Thank you.

For this problem. We are asked to find an example of a nonlinear function with no critical points. So if we have no critical points, then that means that we have to have that the gradient of F exists everywhere. So we have to we must have that gradient gradient of F exists for all X in our two or however dimensions were in. So he could write that as R. N. But we would or rather we could say and we have to have that the gradient of F never equal zero for any X in R N. So we could just read that as for all X and R N again here. So one way that we can do this is create something such that the first partial derivatives are constants. But we are asked to find something that is a non linear function that satisfies this. So instead, well, E to the power of X Never or will never equal zero. And same thing with Eades the power of why no value of X will make either of those equal zero. So a non linear function which has no critical points could be F equals just eats power, Vax times E. To the power of why there's no value that will make this equal to zero and there is no value for which the derivative will not exist. So I realized that actually hear the derivatives in that example, the derivatives would be each power vaccines, power Y and its power Y eats power of X. So it is it's own derivative but using its power backs just as an example of something that never equal zero. So there we have an example of a function that satisfies the requirement.


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