5

9,.09 Points]DETAILSSCALCET9Determine whether the integral is convergentKx 1 (x2| I 2)7 dxl...

Question

9,.09 Points]DETAILSSCALCET9Determine whether the integral is convergentKx 1 (x2| I 2)7 dxl

9,.09 Points] DETAILS SCALCET9 Determine whether the integral is convergent Kx 1 (x2| I 2)7 dxl



Answers

Determine whether each integral is convergent or divergent. Evaluate those that are convergent.

$ \displaystyle \int_0^9 \frac{1}{\sqrt[3]{x - 1}}\ dx $

In this problem were given the improper integral one over X minus one to the 1/3 from 0 to 9 and were asked to determine whether this integral is convergent or divergent. So in this case, neither of our bounds are discontinuous. But this integral is discontinuous at X equals one. If we plug X equals one in, we get 1/0, which is undefined. So I'm going to split this integral up into two and a girls, one being from zero 21 of our integral plus one that goes from one to nine of our integral. So solve this since we have to, and girls that are the same besides the bounds. I'm gonna begin by just solving the indefinite integral one over the cube root of X minus one D x. So to solve this, we're going to use a use substitution where u equals X minus one and d you equals D X. And if we plugged that into our integral, we get the integral of one over the cube root of you. Do you? And if we saw this, we get three halves, huge, the 2/3 plus c. And if we put back in our value for you. We get three halves times X plus one to the 2/3 plus C. And finally, if you plug back in our bounds for both of our integral, we're going to get three halves X minus one to the 2/3 from 0 to 1. Plus three have times X minus one to the 2/3 from 1 to 9. And finally, I'm going to take the limit of this and plug in those bounds. So I'm going to start with this first integral. So if we just take the limit of that, we get the limits. As T approaches one from the left of three have Times team minus one. The 2/3 minus three halves times negative one. And if we put in one, we get three halves. Oops. We re write that we get three halves as our answer, and if we go ahead and do our other one, we will get the limit as T approaches one from the right of three halves times four minus three halves. Times T minus one to the 2/3. And again, if we plug in our value for T, we get six. So if we go ahead and plug this in, I accidentally added a minus. Sign here, so I'm gonna go hand race out so we actually get negative three halves here. My apologies. If we go ahead and add these together we get negative three halves plus six, which equals negative three halves plus 12/2, which equals nine halves in This means that our integral converges to nine halves.

Using the comparison theory test we have the insignia From 0 to Infinity. Eggs divided by X. Cube Bloods one. The eggs to be less than or equal to the integral from 0 to 1. You have eggs divided by S. q. Plus one the X Plus the bigger from one to infinity. You have X Divided by Esky Blood. zero the S. So we have there is infinity X divided by X. Cube Last one. The eggs to be less than the integer from 0 to 1. You have X divided by X. Key platz one the X plus this parts would give us an integer from one to infinity. You have one divided by X squared the X. So this is going to be from 0 to infinity. Eggs divided by x cubed plus one the X. The X less than or equal to. You have been Ciga From 0 to 1 X. Divided by S. Q. Plus one the X. So this interior will give us plus. So I see this would give us minus one divided by X. The interval from one to infinity. So then We have the instagram from 0 to infinity. You have eggs Divided by S. q. Plus one. The eggs less than or equal to this integra Which is 01, eggs Divided by S. Cube, last one the X. Glass. This would give us one divided by -1 divided by Infinity Plus one divided by one for this part. So then you have this eggs divided by S. Key plus one. The eggs TV less than or equal to the integer from 0-1, eggs divided by S. Q. Plus one, The X. Plus one. So you notice that the right hand side so you realize that this this is fine nights Finite on the Interval 01. And here is the lifts. The left is finally because it is laser, so this is fine nights because it is less done this. Okay, so then this implies that so we can conclude and say that they in figure converges.

For this probably want to find values of K. Such that the integral from one to infinity of one over x rays to KD X converges. Now the integral from one to infinity of one over x rays to KD X. This is equal to the integral from one to infinity of x rays and negative KD X. Now, since we have an improper integral, then we have the limit as T approaches infinity of the integral from wanted T of x rays and negative KD X. And then integrating that gives us limit as T approaches infinity of ex recent negative K plus one over negative K plus one evaluated from quantity. That's the same as one over one -K times the limit S T approaches infinity of x rays to one minus K, evaluated from wanted T. No, it is X is equal to T. Then this is equal to 1/1 minus K times the limit. As the approaches infinity of T race to one minus k minus one and if you take the limit of this we will get 1/1 minus k Times Infinity raised to one -K -1. Now for this factor one minus k cannot equal zero or it will become undefined. So this means that k cannot equal one. And for this to be convergent we need to find finite value for the integral. And to do that the exponent for infinity must be a negative value. So one -K has to be less than zero means that key has to be greater than one to be convergent. Therefore Que has to be greater than one or okay. Must be in the interval want infinity for the improper integral to converge.

Today we're going to solve problem, but three in the zero to mine. One day we're two groups off. Eggs minus one. The X claiming do you think sto one minus zero to t one. Divided by que group off X minus one be It's plus You mean do you tend to one plus? Did too. Line one. Do it, Please. Que boot off X minus one The X It is undefined at Texaco toe one. We split it up here. So limit do you? Tends to one minus three by two X minus one by three zero Duty which is equal to three by two Limit He attends toe one minus T minus one. Hold the part two by three minus minus one or the part two by three, which is equal to three by two in tow. Zero minus one. The Jessica toe minus three by two. Then integral limit He tends. Took one plus three. Betty Boop X minus one to buy three Did to nine three by two Limit. They tend to toe one plus nine minutes from Google for two by three. Yeah, Peter


Similar Solved Questions

5 answers
LJEe "HeMk forthe Broduc from tne Grcenas utane (rarz _t deneErllnk Eoirt 130I! WWA LaclertC^nat Fd Auete
LJEe "HeMk forthe Broduc from tne Grcenas utane (rarz _t deneErllnk Eoirt 130 I! WW A Laclert C^ nat Fd Auete...
5 answers
Synthetic steps to make the following compound Using an acetoacetic ester synthesis, suggest . materials and reagents. (5 marks) from acetoacetic ester and any other appropriate startingCHz
synthetic steps to make the following compound Using an acetoacetic ester synthesis, suggest . materials and reagents. (5 marks) from acetoacetic ester and any other appropriate starting CHz...
5 answers
WeDWouk : 01Z31-05 SP18 : ReOopta 10 Homtoedt hilledUreeletudurad duxtoneduf4,0h40/2/123 ~05-SpiqF LonanneCret hajCentetd Cco c_tezs (=olt
WeDWouk : 01Z31-05 SP18 : Re Oopta 10 Homtoedt hilled Ureeletudurad duxtoneduf4,0h40/2/123 ~05-SpiqF Lon ann e Cret hajCentetd Cco c_tezs (=olt...
4 answers
Which histogram depicts higher standard deviation?[[Choose the correct answer below:Histogram depicts the higher standard deviation, because the distribution has more dispersion:B. Histogram depicts the higher standard deviation, because the bars are higher than the average bar in a. D. Histogram depicts the higher standard deviation, because the distribution has more dispersion_Histogram depicts the higher standard deviation , since it is more bell shaped
Which histogram depicts higher standard deviation? [ [ Choose the correct answer below: Histogram depicts the higher standard deviation, because the distribution has more dispersion: B. Histogram depicts the higher standard deviation, because the bars are higher than the average bar in a. D. Hist...
5 answers
Magnitude of the figure coil of135 turns and diameter Long solenoid has U 224 2 the solenoid turns/cm the coil U U currenti outside the solenoid as shown in the 1.5A; its what is the radius Is1.8 cm_Ad666 1 1 0 6 Solenoid
magnitude of the figure coil of135 turns and diameter Long solenoid has U 224 2 the solenoid turns/cm the coil U U currenti outside the solenoid as shown in the 1.5A; its what is the radius Is1.8 cm_A d666 1 1 0 6 Solenoid...
4 answers
Consider the initial value problemiKHHHHLHEHLE olislob Fy(@) HhlThe approximation of y(0. 3) bylusing Euler' $ method With hMmHO.1 is most nearhy1.0293.55320.990031.3688
Consider the initial value problemi KHHHHLHEHLE olislob Fy(@) Hhl The approximation of y(0. 3) bylusing Euler' $ method With hMmHO.1 is most nearhy 1.029 3.5532 0.99003 1.3688...
5 answers
5. Mark's class just took the admission test for business school averaged 83.4. Chapter 10 Data Set 2 contains the populationr and scores for the 10 other classes in Mark's university: How did class do? Marks
5. Mark's class just took the admission test for business school averaged 83.4. Chapter 10 Data Set 2 contains the populationr and scores for the 10 other classes in Mark's university: How did class do? Marks...
5 answers
Dy Find if y = V1 + sin2x dx7. Sketch graph of y2 = x3 12x find the coordinates of the points on the graph of y2 =x3 1Zx at which the tangent line is horizontal_
dy Find if y = V1 + sin2x dx 7. Sketch graph of y2 = x3 12x find the coordinates of the points on the graph of y2 =x3 1Zx at which the tangent line is horizontal_...
4 answers
Prove the following: Write your arguments clearly and legible. Prove that if A is row equivalent to B, then B is rOw equivalent to A. If Ais nonsingular; show A' is nonsingular and (A' )-' = (4-'y
Prove the following: Write your arguments clearly and legible. Prove that if A is row equivalent to B, then B is rOw equivalent to A. If Ais nonsingular; show A' is nonsingular and (A' )-' = (4-'y...
5 answers
Find the component form of $mathrm{v}$ given its magnitude and the angle it makes with the positive $x$ -axis.$$|mathbf{v}|=2, quad heta=150^{circ}$$
Find the component form of $mathrm{v}$ given its magnitude and the angle it makes with the positive $x$ -axis. $$ |mathbf{v}|=2, quad heta=150^{circ} $$...
5 answers
Cantis XC QuestionKandidt In acetone (CHCOCHJl? TntmWnkch Kould te XEl the slwest2 Dromeh aanc Aromu- 3-entity EulieLLorcuol 'ncurnoncthintQucstionmcn value Is the AH valyr for Uie reaction shawn?Mnttu MIALne4ndLiLEnSQucstlonWnidnunnOanemlponal col Emunel hcurd ntom;[email protected]
Cantis XC Question Kandidt In acetone (CHCOCHJl? Tntm Wnkch Kould te XEl the slwest 2 Dromeh aanc Aromu- 3-entity Eulie LLorcuol 'nc urnoncthint Qucstion mcn value Is the AH valyr for Uie reaction shawn? Mnttu MIA Lne 4nd LiLEnS Qucstlon Wnidnunn Oane mlponal col Emunel hcurd ntom; Actneeaet De...
5 answers
Sketch the Born-Haber cycle for MX, and then calculate the electron affinity of X from the following data for MX M, metal; Xis a nonmetal in VIIA group. X2 bond energy 309 kJ/mol; AHf (MX) 500 kJ/mol;_ AHsub(M) 139 kJ/mol; IP1(M) 6,.54 eV; and U--1352kj/mol.
sketch the Born-Haber cycle for MX, and then calculate the electron affinity of X from the following data for MX M, metal; Xis a nonmetal in VIIA group. X2 bond energy 309 kJ/mol; AHf (MX) 500 kJ/mol;_ AHsub(M) 139 kJ/mol; IP1(M) 6,.54 eV; and U--1352kj/mol....
5 answers
1 UIS(1 point) Let f (x) 4sin x + 6 cosThen f' (x)24/(4sin(x)+6cos(x))^2The equation of the tangent line to y = f(r)at a = T 6 can be written in the form y mx + b where m 24/(4sin(pi/6)+6cos(pi/6 and
1 UIS (1 point) Let f (x) 4sin x + 6 cos Then f' (x) 24/(4sin(x)+6cos(x))^2 The equation of the tangent line to y = f(r)at a = T 6 can be written in the form y mx + b where m 24/(4sin(pi/6)+6cos(pi/6 and...
5 answers
Arrange the following Newman projections of bulane In order of increasing energy (decreasing stability).H;CCH,CH3HCH;CH, CHaH HscHHcIv
Arrange the following Newman projections of bulane In order of increasing energy (decreasing stability). H;CCH, CH3 HCH; CH, CHa H Hsc H Hc Iv...
5 answers
Question 3 (1 point)The sales trend has been modeled as: Sales-3*t+100, where t= time in quarters, beginning in Q1 2010. Seasonality for the four quarterly periods is given in the table below: Find the seasonalized forecast for Q1 of 2013. Quarter Seasonal Factor Quarter #1 1.1000 Quarter #2 0.9000 Quarter #3 0.9000 Quarter #41) 196.952) 133.3152.904) 156.00
Question 3 (1 point) The sales trend has been modeled as: Sales-3*t+100, where t= time in quarters, beginning in Q1 2010. Seasonality for the four quarterly periods is given in the table below: Find the seasonalized forecast for Q1 of 2013. Quarter Seasonal Factor Quarter #1 1.1000 Quarter #2 0.9000...
5 answers
Question 3, Cell Structure and OrganellesB) Plant and animal cells both have secreted extracellularcomponents that help support the cells and promote survival.Contrast these components in each type of cell and explain how thecomponent benefits cells in the organism.
Question 3, Cell Structure and Organelles B) Plant and animal cells both have secreted extracellular components that help support the cells and promote survival. Contrast these components in each type of cell and explain how the component benefits cells in the organism....
5 answers
437.5 OC, the equlibrium constant Ior reacton 2 Alal Clg) iK - 3.78 * 10 ~ Hthe equilbrum corcuntrtins 0 B endC FurnectNe 240 x 10-1Mand 4.30x 10 # M the equtbrium concontralion ofA E 048 G0M 0b.0.451 M Oc 476M 1.0.206 M Inone d tho above
437.5 OC, the equlibrium constant Ior reacton 2 Alal Clg) iK - 3.78 * 10 ~ Hthe equilbrum corcuntrtins 0 B endC FurnectNe 240 x 10-1Mand 4.30x 10 # M the equtbrium concontralion ofA E 048 G0M 0b.0.451 M Oc 476M 1.0.206 M Inone d tho above...
5 answers
A projectile is launched with an initial speed of 30.0 m/s andat an angle of 60° with the horizontal. Find the (a) horizontal andvertical components of its initial velocity (express this initialvelocity in terms of unit vectors), (b) time of flight, (c) maximumheight reached by the projectile.
A projectile is launched with an initial speed of 30.0 m/s and at an angle of 60° with the horizontal. Find the (a) horizontal and vertical components of its initial velocity (express this initial velocity in terms of unit vectors), (b) time of flight, (c) maximum height reached by the projectile...

-- 0.020172--