5

Find the domain of the functionV16 f(I;y) arcsin(zy) + In(z2 + y" )cos(z-y - 1)Sketch graph of the domain, and then determine whether is it open Or closed_ bo...

Question

Find the domain of the functionV16 f(I;y) arcsin(zy) + In(z2 + y" )cos(z-y - 1)Sketch graph of the domain, and then determine whether is it open Or closed_ bounded or unbounded_

Find the domain of the function V16 f(I;y) arcsin(zy) + In(z2 + y" ) cos(z-y - 1) Sketch graph of the domain, and then determine whether is it open Or closed_ bounded or unbounded_



Answers

In Exercise (a) find the function's domain, (b) find the function's range, (c) describe the function's level curves, (d) find the boundary of the function's domain, (e) determine whether the domain is an open region, a closed region, or neither, and (f) decide whether the domain is bounded or unbounded. $$f(x, y)=x y$$

In this problem we're going to be identifying indicated features of the given function. The first we will be looking at the do mean if the notice all function is really subtraction between real numbers. Therefore, we have a domain that is oh, all numbers of points in the X Wapping And if we add or subtract real numbers, then our result is also a real number. So we can state that deranged is all room numbers. Next we look at the level curves This in the function that we have here, our level course are going to be linear and the hand selected some values for C from negative to to positive too. And as you will notice level curse our old senior with a slope of positive one next to look at the 100 points of our domain. Considering that all the points in the domain are in considered interior points, we can imply that there is no boundary. So in this case, see that there are none. Our domain is the entire X ray plane and that is considered to be opened because every point is an interior point. And it's also considered close because there are no boundary points doing here. It's both open and schools, and lastly is a do mean bounded on bounded again. Since our domain is all points in the X Y plane, it is unbounded.

And this program, we're going to identify the indicated features of the different functions first, look at doing and here we have a rational function on with rational functions we cannot have. Oh, denominator. Equalling here. So what that tells us here for the do mean we can have any number except the ones Where are any point on the X Y clean except the points where X is equal to zero. Our given function generates all real numbers. So our range would be all were numbers we would look at the level curves we noticed is that where sees equal to zero and the level curve is simply the X axis, Uh, where why is equal to zero and when see is negative. What will see the problem that opens down on when it's thieves Positive. We also get a part problem, but this time it opens up. Okay, All right. So with the bones, your points, we have one restriction and our restriction is that X medical to zero, so X equals zero become our boundary night. Our domain in this case is opened because since X cannot equal to zero, there are no points on the boundary line. So all the points are considered to be interior points and our domain is unbounded because the domain does not. Lions had disc of finite radius.

In this problem will be I didn't define indicated features of given function The first look at the do me since we do with the function e we have no restrictions. Hair sore Dellin would be all point in the x went green or the range. First we need to note that the argument negative x squared y squared. The only possible valuably can get here our own less than or equal to zero. And if that is the case, then zero all function people toe one which is the maximum bottling and any of the value will give us a fraction between 011 So here we we can state that the range would be between zero and one where zero is not included. When the great the level curves, What we get in here are concentric circles. I'm based on what we have here. I just know that when C is equal to one, then the level curve with actually the point in the reserve. Otherwise, we have concentric circles centred under origin. The boundary points Um, in this case we have no boundary point because our domain is the entire X Y plane. So therefore, any point would be considered an interior point. And since we have no boundary, um, this can be considered open. But it can also be, um, considered close, since we have no boundary of report can be considered a bunch of point. And finally this Our domain would be considered unbounded. We could It does not lie inside and did okay tonight, radius.

And this problem will be identifying the indicated features of the given function. The first we start with the Dominion. Normally, the sine function has a domain of between negative one on one inclusive. So based on that, we can see that delay number current function would have to be such that why minus X is between negative one on the war on, Just like the range of the in person function is between negative power for two and fire for to the same applies here. That would have negative probably were to listen or equal to see what you're less than or equal to pi over two. When regret the level curves what we get a linear equations and there of the form why equals X policy. Okay, but we must not hair that of the sea has to go between negative Bolani on one. Don't In the found your points far domain would be the question. The absolute value y minus being ableto one remember, up to the value would give us two equations The weaken Seeing that why equal to X plus warm? Why equal X minus one. So these two equations from our boundary point Spence the bound. All the boundary points are included in the domain. Then that would mean that we have a close Interpol here based on the definition. And our domain is unbounded because it does not like incented a disc of infinite off the night. Really? Iss Excuse me.


Similar Solved Questions

5 answers
Shown in Ihe figure is PV diagram of moles of alr, assumed t0 be an Ideal gas undergoing cycllc process. How much heat energy Is iransferred t0 the gas during Ihe isobaric process tnat occurs at pressure of 250 kPa:300Number2QU 1 1QuVolume (LI
Shown in Ihe figure is PV diagram of moles of alr, assumed t0 be an Ideal gas undergoing cycllc process. How much heat energy Is iransferred t0 the gas during Ihe isobaric process tnat occurs at pressure of 250 kPa: 300 Number 2QU 1 1Qu Volume (LI...
5 answers
In the situation shown; what is the magnification?Convex lonsConvox IcngObjectObleci (notvlsible)T0 mmImaga32.5anm
In the situation shown; what is the magnification? Convex lons Convox Icng Object Obleci (notvlsible) T0 mm Imaga 32.5anm...
5 answers
Remaining Time: 38 minutes; 48 seconds:Question Completion Status:Question 2Which of the following Is true for tne function grapned belova?Iim flx) = -2 X-1-Iim flx) = -2 X--1Iim f(x) = 2 X-2+Iim flx) = 3 X-2-
Remaining Time: 38 minutes; 48 seconds: Question Completion Status: Question 2 Which of the following Is true for tne function grapned belova? Iim flx) = -2 X-1- Iim flx) = -2 X--1 Iim f(x) = 2 X-2+ Iim flx) = 3 X-2-...
5 answers
N2 + Zn + 3 2 + u + +u#5.[8pts]ConvergentDivergent Aq
n2 + Zn + 3 2 + u + +u #5. [8pts] Convergent Divergent Aq...
5 answers
42 points 5F6 13.PM:_My_NotesAsk Your TeacherTransverse waves %ith speed 0l 47. Ns areDe produced on Slrelched slring_ (2, What Ihe requirer tension in the string?OQ m lenglh cr s.ring wilh Tala mass ol D6o0 kg is used.Calculate the wave speed the string the tension M/s8,00 N.
42 points 5F6 13.PM:_ My_Notes Ask Your Teacher Transverse waves %ith speed 0l 47. Ns are De produced on Slrelched slring_ (2, What Ihe requirer tension in the string? OQ m lenglh cr s.ring wilh Tala mass ol D6o0 kg is used. Calculate the wave speed the string the tension M/s 8,00 N....
5 answers
For the following function, complete all the steps below;y = 2x2 4x 16a) Find the derivative function.b) Use the derivative to find any local maximums or local minimums_c) Find de second derivative function:d) Use the second derivative to find all inflection points_
For the following function, complete all the steps below; y = 2x2 4x 16 a) Find the derivative function. b) Use the derivative to find any local maximums or local minimums_ c) Find de second derivative function: d) Use the second derivative to find all inflection points_...
5 answers
[Revlan Topkcs][Rofcronccb]Use the Relcrenccs ( ACCess important valucs if nceded for this question:For the reactionNHCl(aq)NH;() HCI(a4)AG" 64,8kJ and AH? 86.4 kJ at 273 K and mun;This reaction is (reactant; product) favored under standard conditions ut 273 K The entropy change for the reaction of 4.6} moles OfNHCI(Q) at this temperaturc would be JIK
[Revlan Topkcs] [Rofcronccb] Use the Relcrenccs ( ACCess important valucs if nceded for this question: For the reaction NHCl(aq) NH;() HCI(a4) AG" 64,8kJ and AH? 86.4 kJ at 273 K and mun; This reaction is (reactant; product) favored under standard conditions ut 273 K The entropy change for the ...
5 answers
407 26,55go Mg (POAh are dissolved to make 500.0 mL of solution: What Is the molarity or thts solution?(b) 5.00 mL of this solution are then diluted to 250.0 mL What is the molarity of the final solution? (c) What is the concentration (molarity) of the magnesium ions in this final solution?
407 26,55go Mg (POAh are dissolved to make 500.0 mL of solution: What Is the molarity or thts solution? (b) 5.00 mL of this solution are then diluted to 250.0 mL What is the molarity of the final solution? (c) What is the concentration (molarity) of the magnesium ions in this final solution?...
5 answers
A series audio circuit is shown in Fig. 9.78(a) What is the impedance of the circuit?(b) If the frequency were halved, what would be the impedance of the circuit?
A series audio circuit is shown in Fig. 9.78 (a) What is the impedance of the circuit? (b) If the frequency were halved, what would be the impedance of the circuit?...
5 answers
Question 63.5 pelntsFind at the point (4,1) on the curve 4vx -3xv+v'=-3. 0x0A 4 08 1/8 Oc-8 00-1 06-1/4
Question 6 3.5 pelnts Find at the point (4,1) on the curve 4vx -3xv+v'=-3. 0x 0A 4 08 1/8 Oc-8 00-1 06-1/4...
1 answers
The pH of gastric juice is about 1.00 and that of blood plasma is 7.40. Calculate the Gibbs free energy required to secrete a mole of $\mathrm{H}^{+}$ ions from blood plasma to the stomach at $37^{\circ} \mathrm{C}$.
The pH of gastric juice is about 1.00 and that of blood plasma is 7.40. Calculate the Gibbs free energy required to secrete a mole of $\mathrm{H}^{+}$ ions from blood plasma to the stomach at $37^{\circ} \mathrm{C}$....
5 answers
Find the indicated matrix:Find -3(4- B)1 9 A=|92 8 and B = |: 8" 2|3 479 129 3 27 51 4 3651 15] 24 18]27 36S1
Find the indicated matrix: Find -3(4- B) 1 9 A=|9 2 8 and B = |: 8" 2| 3 47 9 12 9 3 27 51 4 36 51 15] 24 18] 27 36 S1...
5 answers
Next quastijnOesnrunctlon LvaluatIonGiren thc functlon Rcund ans ven27(1,91' cualuste rach llic' Fnllovlne IFe nealest hundredth 45 neededQelanreldntetetldn
Next quastijn Oesn runctlon LvaluatIon Giren thc functlon Rcund ans ven 27(1,91' cualuste rach llic' Fnllovlne IFe nealest hundredth 45 needed Qelanreld ntetetldn...
5 answers
In the laboratory you are given the task of separating Ba2+ andFe2+ ions in aqueous solution. For each reagent listed belowindicate if it can be used to separate the ions. Type "Y" for yesor "N" for no. If the reagent CAN be used to separate the ions,give the formula of the precipitate. If it cannot, type "No"Y or NReagentFormula of Precipitate if YES1. fill in the blank 1Na2SO42. fill in the blank 3K2CO33. fill in the blank 5Na2S
In the laboratory you are given the task of separating Ba2+ and Fe2+ ions in aqueous solution. For each reagent listed below indicate if it can be used to separate the ions. Type "Y" for yes or "N" for no. If the reagent CAN be used to separate the ions, give the formula of the p...
5 answers
5. Draw a food web with the following names of organisms and arrows between: owl, grasshopper, grass,rabbit, snake, mouse, hawk, songbird, worm, berry bush, chipmunk
5. Draw a food web with the following names of organisms and arrows between: owl, grasshopper, grass,rabbit, snake, mouse, hawk, songbird, worm, berry bush, chipmunk...
4 answers
Point) Let r(t) = t sin(t)i + t cos()k + 2 8/2j 3 for t in [0,n].Find the unit tangent vector to the curve given by r.Find the length of the curve traced out by r.
point) Let r(t) = t sin(t)i + t cos()k + 2 8/2j 3 for t in [0,n]. Find the unit tangent vector to the curve given by r. Find the length of the curve traced out by r....
5 answers
Find the mean value of the function 3 Tt y = 2cos X on the interval [2 (5 marks)
Find the mean value of the function 3 Tt y = 2cos X on the interval [2 (5 marks)...
5 answers
The figure shows lhe graph of the hyperbola Find the volume of the solid by rotating the region between the upper branch of the hyperbola and about the y-axis(Express numbers exact form. Use symbulic notation and fractions where needed )Voume:
The figure shows lhe graph of the hyperbola Find the volume of the solid by rotating the region between the upper branch of the hyperbola and about the y-axis (Express numbers exact form. Use symbulic notation and fractions where needed ) Voume:...

-- 0.022194--