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An Even function f(x) has period T atxe[12;15]Find the value of - f(5) if ffx)4011,44...

Question

An Even function f(x) has period T atxe[12;15]Find the value of - f(5) if ffx)4011,44

an Even function f(x) has period T atxe[12;15] Find the value of - f(5) if ffx) 40 11,44



Answers

25 - 48 Find $f$.
$$f^{\prime}(t)=4 /\left(1+t^{2}\right), \quad f(1)=0$$

Okay, so we're being asked to find F and were given a promise to use people there for over one plus two squared and the effort one zero. So let's get right into it. So we're checking the integral are for over one foot two squared. Oh, no, thanks. Oh, one plus two square DT. We can pull out a common factor for injected into your one over one foot. He's squared DJ, and this is going to be equal to four Casian and worse, or tea for some constant C. And that's it. That is our function. And so now we're told that half of one s so it's good unplugging ones of four ten in words of one plus C is equal to zero. So they're mean. Well, tell members of one's private forces before Ty over four or the fourth cancel and it will be prosecuted because zero and C is equal to negative. Hi. So that means our function after Max, it is going to be going to four tangent and worse off key. This is I'm sorry again turned t minus pi, and that is our function

We're doing a fallen function of property is able to 4/1 post a square When I, for one as you stare, were asked to find out 15. So start off with we need to find 15 So we know that 1/1 plus e scored that interview over that just octane of So we have four. It harms our tune poverty plus a binge every constant, of course. And then we'll somehow effort want is equal to zero so we can sit on her own at zero is able to for it to our tin. But one plus e. We know that for 10 of one is just part over four plus c so we get zero is equal to pi plus C, and so C is equal to 90 of pie. Then we can plug it back into our function to get for our 10 4 times are tan of tea minus part as effort e

Three were given an equation off Dashti with initial condition. Based on these two conditions, we need to find out. So let's integrate. Both sides have dashed T d t would be a route t d t on over here we have DT or square. We need to integrate this using the somewhat difference rule off integration. We are integrating all the terms separately. Now, using the power rule here, the integration will be power will be added by one on we divide by the same power on this can be written as theories to the power minus one over to BT taken enumerators of the power becomes negative So this becomes two or three times three days to the poultry over two plus three days to the ball one or 2/1 over two means two will come here plus C no el 40 This is at 40 means definitely placed by zero and easy placed by four. So four square root the stool to Cuba's aid Foursquare routers to plus C So see comes out as this will be minus e and this will be, uh, 16/3 plus four. So this comes out as 28/3. This is minus. C. Soc will be minus off 28/3, which we placed over here. So the final equation comes out for F S two or three. I am Steris to the poetry or two plus two theories to the about one or two is nothing but a booty plus C. Soc is 28 or three. So this is the final answer.

High River Pretty via going bizarre problem number man here for 50 years. Given us, do you do it? But days, class plus foot. And because what you have to find f off D minus, which is equals. And for B minus one replaced D by D minus one B minus from they were by U minus. Wanda was square breath, foot D minus weren't there. But these class minus two a day Let's going bless foot, which is because the miners were They were, but they've square minus to B plus. But I understand off a question. Thank you.


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