5

The graph of y = f(x) is defined for all xz 0 contains the point (0, 1), dy = 4Vxy and f(x) >0 for all x. Find y. dx...

Question

The graph of y = f(x) is defined for all xz 0 contains the point (0, 1), dy = 4Vxy and f(x) >0 for all x. Find y. dx

The graph of y = f(x) is defined for all xz 0 contains the point (0, 1), dy = 4Vxy and f(x) >0 for all x. Find y. dx



Answers

Find $\int_{0}^{4} f(x) d x$ for each graph of $y=f(x)$

In this question, you're given to crafts of the function F of X and were asked to find the integral from 0 to 4 of of of X dx in each case. So first off, we know that this interval is basically asking us for the area under the curve. So in between the curb and the X axis between X equals zero and X equals four. So for both of our grafts, we have a pretty simple geometries will be able to do this pretty easily. So when I first looked at craft A, I can see that the area between the graph on the X axis forms a triangle. So all I need to do is use the formula for the area of a tranquil. So I know that that is 1/2 turns the base of the tranquil times, the height of the triangle. So for this triangle, I will have 1/2 comes the base of four. We're going from X equals zero tax equals four times two because the highest point of the triangle is too. This works out to be four to the integral from 04 of FX DX for part A is equal to four in Part B were asked to do the same thing. We just have a new graph. Found this case. I realized that I have two triangles. I have this first triangle that I'm shaving in blue. I have the second triangle that I'm shading and in green. So to find the total area between the curb and the X axis, we have to some the area of these two triangles together. So for my first triangle again, triangle formula is 1/2 times base times height for the area. That first triangle has a base of three. It's been through X equals zero to X equals three, and its height is three as well. So this is equal to 4.5. And for my second triangle, the Green Triangle again using the formula for the area of a triangle by 1/2 times these times height. The base of this triangle is one because we're going from X equals 32 x equals for that as a height of one to the area. That second triangle is 1/2 now, just summing these together to get her final answer. The total area, under the curves of ethnic tax from X equals 0 10 x equals four will be shy for craft beer

This problem we're dealing with the function effects is it will execute minus X square minus arts. Yeah. Plus one. And we want to find where this function is positive, where it's negative and then sketches crap Now in order to find where it's positive and where it's negative. When you find where it's equal to zero first, let's let's set this april zero and then solve it. So it's all this. Let's do this part here in this first group, they have an X squared in common. So let's take an X squared out. When I pulled out. That loses with x minus one. Found that next trip. Let's pull a negative one out and that will leave us with x minus one. And so this is x minus one. I'm jack squared minus one. Yeah, So this is our finest juan times X minus one times X plus one which is x minus one squared times are exposed to. And that's what this craft and that's what this function should be. X minus one square times X plus one. This means that this is going to be zero at negative one and one those are are zero. And so it's putting our values here. It's probably a negative too. We have two minus one is negative. Three squared is positive. They have two plus one is negative. It's over naive to that's negative in between her. When we put in 00 minus one is negative one, they once were positive zero post once positive positive times a positive is positive. And we put in a big number over here like 100 100 minus one squared is positive, 100 plus one is positive. And so it's positive over here free. That's what this means. Is that f of X is greater than zero from negative 1 to 1 and 1 to 100. I'm sorry, in one to infinity because that goes on forever. And if if X is less than zero then from negative infinity today you have one. Uh huh. Now if we use this to graphic. Yeah. Mhm. Okay, it's positive from negative 1 to 1 and want to infinity positive from negative 11 and want to infinity that's negative elsewhere. And so it's something like this.

In the problem we have F W S X. Upon earth does X equal wanna so integrating it? We have Ellen after sex equals X plus C. Our Since FDR zero is equal to one. Therefore Ellen Fds zero equals zero plus C. Our Ln one equal C or C equal zero. So further we have FDS X equal power X plus C. Now every six equal it for X plus eight parsing. That is equal to eat for X plus K. Or rather it SK one. Now F X becomes it bore X plus cakes plus. Okay to give an X plus kato. So we have F of zero equal you pour zero plus kevin into zero plus K two. Or we have been given the value of F of zero. So it is zero. That is equal to one Plus Kato. Are gaps. This gives us K two equal -1. So we have FDA zero equal eat power zero plus K one. Now here one equals 1 plus K. one. That implies given equal zero. Therefore f of X equals you. The bar x minus one. So area is given as a present 0-1, 84 x minus one plus one dx. Or it is equal to eat for x 0- one, which gives us for 1 -840, which is equal to E -1. And this is the answer to the problem. So here is the scarf because we have also to see the car. So the car is this one mm So here is the car. And according to the curve, we have made the find out area. So this carve is four, You bore X -1 and this is the car for one. So we have this as the answer to the problem.

In this question were given the function effects is equals to one of our four X cubed minus two. Our tool to find values off X that would make the function greater than zero and less than zero. So to find that we have to find the value of X that would make effects. Walsh is, er one of our four x. You minus two is equal to zero. One of our four x cube equals two to exit goes to to. So if when X equals to do effects is equal to zero. So therefore yes, when x is greater done. So it fix is greater than zero. When X is less than two effects, it's less than zero. This is the answer. We'll also go to sketch a graph off the function on. And this I'm gonna head on. Used a graph incognito to a graph. That's so this is gonna be a graph off the function


Similar Solved Questions

5 answers
Juublz inleenl LOLOCnuulex th :Oluie ofthc solid undcr 4 inudc Ibrylingt +y %y = (I0 prnls}Lmuenh T
Juublz inleenl LOLOCnuulex th :Oluie ofthc solid undcr 4 inudc Ibrylingt +y %y = (I0 prnls} Lmuenh T...
5 answers
Use elementary row operations to reduce the given matrix to row echelon form and reduce [3 -4 72 8 8 (a) row echelon form 35(b) reduced row echelon form
Use elementary row operations to reduce the given matrix to row echelon form and reduce [3 -4 72 8 8 (a) row echelon form 35 (b) reduced row echelon form...
5 answers
Q4) How many mls of 4.0 M Sucrose solution and water do you need to make 10 mls of a) a 0.8 M and b) 0.6 M Sucrose solution? [MIVI-M2V2]
Q4) How many mls of 4.0 M Sucrose solution and water do you need to make 10 mls of a) a 0.8 M and b) 0.6 M Sucrose solution? [MIVI-M2V2]...
5 answers
9x2 Find the absolute extrema of f(x) on the interval [-2, 2]. X-3maximum;minimum;
9x2 Find the absolute extrema of f(x) on the interval [-2, 2]. X-3 maximum; minimum;...
5 answers
(2pts) Verify that the differential equation nOt exact appropriate integrating factor and solve the equation , (Spts) Find an (3pts) Find algebraically the interval of definition of the solution. 2ty In(t2 +1)y' = 0 y(5) = 0 -2t - (2 _ t2+1
(2pts) Verify that the differential equation nOt exact appropriate integrating factor and solve the equation , (Spts) Find an (3pts) Find algebraically the interval of definition of the solution. 2ty In(t2 +1)y' = 0 y(5) = 0 -2t - (2 _ t2+1...
5 answers
Question 11 (1 point) What is the electron configuration of a sulfur atom (dont try to mess with exponents- just put 152252 and so on)
Question 11 (1 point) What is the electron configuration of a sulfur atom (dont try to mess with exponents- just put 152252 and so on)...
2 answers
V H HEnnenn L U 1 mna dgn: Round Your standard narral varlable Maraeum 2 declmal 1 (You may IInd It useful2
V H HEnnenn L U 1 mna dgn: Round Your standard narral varlable Maraeum 2 declmal 1 (You may IInd It useful 2...
5 answers
10. Sketch for 31 < * < 31. (4 marks)y = sin 2x y = cos} x
10. Sketch for 31 < * < 31. (4 marks) y = sin 2x y = cos} x...
5 answers
Consider the equilibrium system described by the chemical reaction below; which has a value of Kc equal to 0.042 at a certain temperature_ If 2.860 g of PCIs initially decomposes in a 700 mL closed container; what will the equilibrium concentration of PCis be?PCI(g) PCI(g) Cl,(g)
Consider the equilibrium system described by the chemical reaction below; which has a value of Kc equal to 0.042 at a certain temperature_ If 2.860 g of PCIs initially decomposes in a 700 mL closed container; what will the equilibrium concentration of PCis be? PCI(g) PCI(g) Cl,(g)...
5 answers
Zupneje ndocreasing Lqustoni Vi sequence; decreasi defined recursivelyfor n 2 Then X
Zupneje ndocreasing Lqustoni Vi sequence; decreasi defined recursively for n 2 Then X...
5 answers
In an isotherma reversible expansion at 318C, an ideal gas does 25 of work. What is the entropy change of the gas (in J/K)?JK
In an isotherma reversible expansion at 318C, an ideal gas does 25 of work. What is the entropy change of the gas (in J/K)? JK...
5 answers
Seen that the cquation ofof the displacement as a function of time squared we made plot Consider what would happen will bc graphing time squared. Let us take the ((Onfor the above equation. So on the time axonst with constant acceleration of +4 m/s? in the %-direction case of an object that starts from rest the axes what Is being plotted against Complete the table and Braph below: (Look carefully at = what?
seen that the cquation of of the displacement as a function of time squared we made plot Consider what would happen will bc graphing time squared. Let us take the ((Onfor the above equation. So on the time axonst with constant acceleration of +4 m/s? in the %-direction case of an object that starts ...
5 answers
The wavelength of red light from a helium - neon laser is 633 nm in air and 479 nm in a medium of index of refraction n. The speed V and the frequency f of light in the given medium are: (Given: c = 3 x 10^8 mls, and 1 nm = 10^-9 m)v = 2.27*10^8 m/s;f = 6.26 x 10414 Hzv = 2.45 * 10^8 m/s ; f = 4.74x 10414 Hzv =2.64x 1048 m/s;f = 4.74x 10414 HzV =2.64x 1048 m/s;f = 5.39 x 10414 Hzv =2.45x 1048 m/s; f = 5.80 x 10414 Hzv = 2.27* 10^8 m/s; f = 4.74x10414 Hz
The wavelength of red light from a helium - neon laser is 633 nm in air and 479 nm in a medium of index of refraction n. The speed V and the frequency f of light in the given medium are: (Given: c = 3 x 10^8 mls, and 1 nm = 10^-9 m) v = 2.27*10^8 m/s;f = 6.26 x 10414 Hz v = 2.45 * 10^8 m/s ; f = 4.7...
5 answers
5 JlawBetween any two real numbers there is an rationalnumber:10 @bui aw @Oubji g231j51300 @tlallTrueijb pFalse
5 Jlaw Between any two real numbers there is an rationalnumber: 10 @bui aw @ Oubji g231j51 300 @tlall True ijb p False...
5 answers
3 Venn Use [ ithe I 1 Venn 1 pul answe the next 2 [ questions;Simplify each of the following expressions 8y 16y2 712 and deterine all restrictions:59 9-3 #
3 Venn Use [ ithe I 1 Venn 1 pul answe the next 2 [ questions; Simplify each of the following expressions 8y 16y2 712 and deterine all restrictions: 59 9-3 #...
5 answers
For cachand of x SULJAI4 (P)43 ()expressions; find 1"y differentiation folpheindi { Usc 4 (a)ry
for cach and of x SULJAI 4 (P) 43 () expressions; find 1"y differentiation folpheindi { Usc 4 (a)ry...

-- 0.024032--