5

Points) Write the function f (2) = 2 a5 the suu of its real aud imagiuary parts: Then uSc the Cauchy RicHa equations t0 show that f is Holomorphie. Vote: It is not...

Question

Points) Write the function f (2) = 2 a5 the suu of its real aud imagiuary parts: Then uSc the Cauchy RicHa equations t0 show that f is Holomorphie. Vote: It is not dlillerentiable (and therelore HOt holomorplic) At 20 = 0 HOI along tic negative axis if we are Using the principal value ol 2- But it is holozuorplic everywhere else.

points) Write the function f (2) = 2 a5 the suu of its real aud imagiuary parts: Then uSc the Cauchy RicHa equations t0 show that f is Holomorphie. Vote: It is not dlillerentiable (and therelore HOt holomorplic) At 20 = 0 HOI along tic negative axis if we are Using the principal value ol 2- But it is holozuorplic everywhere else.



Answers

Fixed Point In Exercises 25 and $26,$ approximate the fixed point of the function to two decimal places. [A fixed point of a function $f$ is a real number $c$ such that $f(c)=c . ]$
$f(x)=\cot x, \quad 0<x<\pi$

Okay. In this question, we want to find the l line l that prostitutes pimps be wanting to be true. The pistol rule. Find door translated like I don't know which positive. Very be to be one. Performing calculations minus two minus one, which is minus three minus one minus four is just minus five. So the point is, in albums, it must be perfectly clear to this line out here. So if you spend a nickel in the Bumble Bee to mind what our victim, this should give you so in one. And Chief Well, I thought that was minus three and Mars by which is even too negative. Three and one and two. Today's long for anyone. We just have this need to name two live and chewed over. So then we just choose a model for into cancer satisfaction. So this is choose end to minus three at an and one is equal cheered. So then you have and it's even true. Five and wise three. So then we're functioned x one x two is even to you and X, which is to be five x one minus three x tooth to this function. Come dysfunction represents all lines with which is parallel to this. Inspected by open ridiculous Inspector. Right here. So to get back online, Ellis on what we need to do except servitude. One of these points in anticipation. So we can either pull minus two miles. One no one in for closer this case. It was wonderful. A 14 executive flats, as one wishes you find minus three times What was she 12. This is my son Thio Online l is along. L is Why x one? Twice three x two 97 Oh, by x one one's three x to just seven is equal to zero.

Here we have f of X y equals E to the X Y squared. Let's calculate the partial derivative of F with respect to X that gives us E to the X Times y squared. Now let's calculate the partial derivative with respect. Why that gives us two y times e to the X. Now we need to evaluate this function these functions at 02 So we get eat zero times two squared. That gives us four and for why we get two times to times E to the zero and that gives us four and that's it.

All right, So this is a tractor to section four. Problem number 19 Um, And for this one, our task is to graphic function with some restrictions. So first off, um, if our function is f of X, half of two has two equal five. The first derivative of the function at two is 1/2 in the second derivative of the function. It too zero. So if we start, we can put are to mark somewhere around there, which means our five mark would probably be about there. So here, this just means that the point two comma five is on the graph. And if that's the case, then that will satisfy Heartwood. So we can put the point to common five right there. And our first condition there is satisfied. For the 2nd 1 We have a prime of two equals 1/2. And this just means that the slope at this point that we've put out has to be 1/2 So that might look if we draw the slope on there, it could look something like that. Um, and that's just arc Tangent line. That's not what the actual graph is gonna look like. It's sort of gonna act as a guideline for this last one. We can go ahead and check that off since the derivative there since our tangent line there as a slope of 1/2. Now, if you look at this last condition, F double prime of two has to be positive. This just means that the second derivative is positive. It too, which means it's curving up and that the slope is increasing. Um says since the slope is increasing, it means we have this point with a slope of 1/2. And that means from there we go on the slope has to be has to continue to increase after that, um so that could be drawn as something like that. Something along those lines. And this works because it is a function. It's continuous, and there's no two y values for every X value. Um, it has a point at two comma five. It's a tinge of line right here as a slope of 1/2 and it is Khan gave up. Its in the second derivative is positive. So this function right year fits our requirements, and that is one possible solution to these

You want to find a function that would yield F of negative two equals two in f of zero equals 10. It had to be linear with just two points. We know that the Y intercept it here would be 10. And we can find the slope the slope is our it's like you could call it why two or F of X two minus F of X one over X two minus x one. So we could say That this is, for instance, 10 -2. That's our outputs over the input, which is eight over to or four. So F of X The slope of four and AY intercept of 10. Now check F of negative to that would be negative. Eight plus 10 is two and F of zero is 10. Here's an example function that way. Have these conditions. Mm


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