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The contour map below shows some level curves of f(x.y). Each level curve is labeled. Assuming that the level curves provide reliable illustration of the general sh...

Question

The contour map below shows some level curves of f(x.y). Each level curve is labeled. Assuming that the level curves provide reliable illustration of the general shape of the function use them to estimate f(2,4) and f(5,1)-

The contour map below shows some level curves of f(x.y). Each level curve is labeled. Assuming that the level curves provide reliable illustration of the general shape of the function use them to estimate f(2,4) and f(5,1)-



Answers

A contour map is given for a function $ f $. Use it to estimate $ f_x(2, 1) $ and $ f_y(2, 1) $.

So we want to find the values of FX of 21 and why of 21 using the Contour map given so we know the definition of a derivative. So first, let's find f x of 21 So we know we have the limit as a true purchase zero, um, f of X plus age. So our exes to in this case, so two plus h comma one. Really the why the same? Because this is an extra evidence. A minus fx. Why all over H? So, looking at the values we can see on the contour map, it's gonna be helpful to take age equals negative one on one. So first, let's do negative one s. So we would get the limit As H approaches. Zero f of two minus one would give us f 11 minus f of 21 all over negative one. And by looking at the contour map, we can see that Ethel 11 is seven. Effort to one is 10 divided by negative one. This gives us a value of three. If we do one, we get the limit as h goes to zero. Uh, we're gonna add one. This time. So efforts 31 minus f of 21 over one, which gives off of 31 gives us 14. Then we still have 10 on H is one. So this gives us a value of four. So therefore we can conclude, Um, a good estimate of FX of 21 is about the average of these two, which is 3.5. So now we're gonna do the same thing for F y. So we're gonna D'oh! Uh, h equals negative one on one. Let's use minus one. So this time we're gonna alter the, uh Y coordinate. So s of a two and then one minus one minus f of 21 all over. Negative one. So that's just 20 So f of 20 gives us 12 f of 21 still 10 over negative one, giving us two over minus one, which is negative, too. For each equal toe one, we get the limit as each goes to zero. So now we're gonna add one to the y coordinate. So we have to to minus up to one over one f of 22 gives us eight, and then we still have minus 10 divided by one, which gives us a negative too s. So if we take the average of the two values is just gonna be the same value. So we can conclude that f why of 21 is approximately negative too.

For this problem, we are asked to sketch the level curves for the equations that equals X plus y with C equals negative +102 and four. So what we can do here is first rewrite the equation as C equals X plus y. Then we can rearrange this to get Y equals c minus X. Now seeing that we can see that our level curves would correspond to Y equals negative one minus X, Y equals negative X Equals 2 -1 and four minus X. So we can see that our level curves are going to be corresponding to a series of just straight lines with different y intercepts. So our first is The first one that I should draw. Actually I'll do the 1 -1 and then actually that was a little bit off there. Then we have the one that passes through just zero. Oops. Then we have the one that passes through two and through four. There we go.

Okay, So if we wanted to draw the level curves and would look something like this Oh, keep in mind that I am not drawing perfect circles simply because I'm not very good. It the fleas. If you can draw them as perfectly as you can so we could know the Contra occur by flooding. F of X coli is equal to see. So expert pulse twice for Zeke with zero extra police Westbury 048 12 and 16 and so on and so on and so forth.

In the problem, we have been given the equation that is F. Of X comma Y. That is equal to Ellen X Square last four White Square. Now, here you have to draw the car for this equation. So we have to draw the contour map of the function. So this is the function, and the contour map of this function is sewn over here. So here we have, this has ex excess, this has Y axis, and this as the Alexis. So this is the contour map of the function. This, since this is the answer to the problem.


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