5

Evaluate3 2 +h ~() lim h->0 h...

Question

Evaluate3 2 +h ~() lim h->0 h

Evaluate 3 2 +h ~() lim h->0 h



Answers

Evaluate the limit.
$$
\lim _{h \rightarrow 0} \frac{\sin 2 h \sin 3 h}{h^{2}}
$$

Plugging in high over to we end up with one minus the cool sign of three pi over tube, which is zero divided by pi over too. This is equal to one divided by pi over to which is equal to two over.

Okay so we need to evaluate this limit using algebra. Notice if we plug in zero directly you will get a division by zero. Let's do some expanding of our numerator. So this is equal to the limit as a church goes to zero. Our denominator is two h three plus H quantity squared this is H squared plus six H Plus 9 -3- each squared is a square nine is 6. H. Last nine. The Plus 9 -9 will cancel. So this is the limit As a church goes to zero. Oh also the H squirts will cancel. So this is 12 age over to H and the ages were cancelled. Probably two is equal six. So this limit Is equal to six.

Okay, so we'll start by, um, expanding our new Merida. So we get three x plus three h minus word minus two x h and then minus h squared. And we also have minus three x and plus X squared. And then that's all over each. And I Let's see if we can cancel anything looking cancel out of X squared as well as the three X. Okay, so we see that we have three terms or meaning, and they haven't h in each turn. So well, factor one of that out of each and in three minus two X and in minus each over h so we can cancel out our each and know that, um, which cannot be equal zero. And now let's use drugs up. So we have three months to x on my style, So that's equal to three minus two x

I see using drugs up. We see that we get division right now. So why don't we expand our powers of three? So I'll just put this into an online calculator to see what I get. Okay, so we have the limit as h approach Joe of experts. H was three to the power of three. Actually, that too. Sorry about that. Okay. So cubing that we get, um, inch cube for three each square x in plus three h equity plus X cube plus six h squared plus Paul H. And then put six x squared plus 12 each first world and in plus eight. And I will subject that with exports to Cuba, that's negative. X cubed minus six x squared, minus 12 at and then minus eggs. And this is all over H. So let's simplify what you have, so we can cancel out a X Q off a six x clay. 12 acts. And okay, now let's factor out. We feed out in each term. We have a H in common to a factor that out. You have the limit as h approach. You don't of age times it squared. Plus three h plus three x word then we have, um, was six h plus 12 um, an implosive Paul all over age. So we feed out our cancels and we should also note that H cannot be equal, though. And now let's use drinks up. Who using dxl. Rh cancels. Since it's equal to down. So every term or h become zero and we're left with three x squared plus 12. That's and in plus.


Similar Solved Questions

4 answers
(40 pt) Consider the integral[ =L' $" V _ e"(r+l/f) drdy _Sketch the domain of this integral. Characterize the boundaries in terms of new variables, u = Iy and 0 = ulx. Show that the Jaccobian of this transformation is92, aqu,2vUse all this to show that [ = %(e - 1)?
(40 pt) Consider the integral [ = L' $" V _ e"(r+l/f) drdy _ Sketch the domain of this integral. Characterize the boundaries in terms of new variables, u = Iy and 0 = ulx. Show that the Jaccobian of this transformation is 92, aqu, 2v Use all this to show that [ = %(e - 1)?...
5 answers
Question 2 [10 points]Find a formula in terms of k for the following determinant:8-8 4 -6 kdet~10 76 7
Question 2 [10 points] Find a formula in terms of k for the following determinant: 8 -8 4 -6 k det ~10 76 7...
5 answers
04Meat woul SMu FMrxt lo sce dislyelmm eeilkncr &iaeled mtE RL mt tlie huutez sumuu krkIimiSvTAOintui010 |Sv
04 Meat woul SMu FMrxt lo sce dislyelmm eeilkncr &iaeled mtE RL mt tlie huutez sumuu krk Iimi Sv TAO intui 010 | Sv...
5 answers
(4pts) Show that Ee(xz) has x?(n - 1) distribution_ (Hint: Calculate moment generating functions_ You may use the fact that the sample mean X and the sample variance S are independent. )
(4pts) Show that Ee(xz) has x?(n - 1) distribution_ (Hint: Calculate moment generating functions_ You may use the fact that the sample mean X and the sample variance S are independent. )...
5 answers
Consider two wire separated by a distance = 2d I,=1A 1z7 2 A Q1. What is the direction of B-field at point A? up; down; C.into the paper; D. out-of the paper; E.B=0Q2. What is the magnitude of the B-field?Ko 4udKo 2ndA. zero300 2ndId03. Now consider point B, what is the magnitude ofthe B-field? Ko Sp0 D. Zuo E: 340 A: znd 6nd nd 6nd 2ud
Consider two wire separated by a distance = 2d I,=1A 1z7 2 A Q1. What is the direction of B-field at point A? up; down; C.into the paper; D. out-of the paper; E.B=0 Q2. What is the magnitude of the B-field? Ko 4ud Ko 2nd A. zero 300 2nd Id 03. Now consider point B, what is the magnitude ofthe B-fiel...
5 answers
Give the structure for the followiug reaction s clcctropnilic neucuun uccure#num only monosubstitution poltts)HNOJ HSO4BrzFeBraNaOCH CHa CH;CH OHNOzHNO3 HzSO4CF3NaOCH CHJCH;CHzOH
Give the structure for the followiug reaction s clcctropnilic neucuun uccure#num only monosubstitution poltts) HNOJ HSO4 BrzFeBra NaOCH CHa CH;CH OH NOz HNO3 HzSO4 CF3 NaOCH CHJCH;CHzOH...
5 answers
QUESTION 14A certain light wave has wavelength of 600 nm when traveling in a vacuum. a) What is its frequency in a vacuum? b) What is its frequency in a medium with index of refraction c) What is Its wavelength In a medium with index of relraction 1.4? d) What Is the speed of the wave In = medlum wilth Index of refraction Please write your answers In the space below and emall your work; For the toolbar; press ALT+F10 (PC) or ALT+FN+FIO (Mac):ParagraphArial14pxx2 Xz
QUESTION 14 A certain light wave has wavelength of 600 nm when traveling in a vacuum. a) What is its frequency in a vacuum? b) What is its frequency in a medium with index of refraction c) What is Its wavelength In a medium with index of relraction 1.4? d) What Is the speed of the wave In = medlum w...
5 answers
Themods? populatlon In Jasper currently on the decline In Jasper Nationa Patk Sorne of the reasans for the population decline Be LMer nuse porasiuc dlsease retum of the wolves the area,and Increased tratfic In the highways:Natch the cause moose population decline the type 0t Imlting (actor using the drop down merCause & Populatlon DecUne Limting FactorLiver IlukeInueasepopulationWclnighivay tafne
Themods? populatlon In Jasper currently on the decline In Jasper Nationa Patk Sorne of the reasans for the population decline Be LMer nuse porasiuc dlsease retum of the wolves the area,and Increased tratfic In the highways: Natch the cause moose population decline the type 0t Imlting (actor using th...
5 answers
1.An element that is a gas at room temperature and highlyreactive most likely belongs to which of the followingfamilies:Alkali metalsAlkaline earth metalsHalogensNoble gases2.Which set of elements are examples of transitionmetals?Al, Na, MgNa, K, RbMg, Ca, SrCr, Fe, Cu3.List two properties common to metals and contrastthose with two properties common to non-metals.
1.An element that is a gas at room temperature and highly reactive most likely belongs to which of the following families: Alkali metals Alkaline earth metals Halogens Noble gases 2.Which set of elements are examples of transition metals? Al, Na, Mg Na, K, Rb Mg, Ca, Sr Cr, Fe, Cu 3.List two propert...
5 answers
Altempts IeltCheck my workBe sure to answer all parts.Determine the number of oxygen atoms in 1.OO kg of water:atoms(Enter your answer in scientific notation )Determine the number of hydrogen atoms in L.OO kg of water:atoms(Enter your answer in scientilic notation )Calculate the mass of potassium carbonate that contains 1.0O mol of oxygen atoms_
altempts Ielt Check my work Be sure to answer all parts. Determine the number of oxygen atoms in 1.OO kg of water: atoms (Enter your answer in scientific notation ) Determine the number of hydrogen atoms in L.OO kg of water: atoms (Enter your answer in scientilic notation ) Calculate the mass of pot...
5 answers
1.How can the center of mass of an object be located at a point outside the object, that is, at a point in space where no part of the object is located?
1. How can the center of mass of an object be located at a point outside the object, that is, at a point in space where no part of the object is located?...
1 answers
Consider a pair of forces, one having a magnitude of 20 $\mathrm{N}$ and the other a magnitude of 12 $\mathrm{N}$ . What is the strongest possible net force for these two forces? What is the weakest possible net force?
Consider a pair of forces, one having a magnitude of 20 $\mathrm{N}$ and the other a magnitude of 12 $\mathrm{N}$ . What is the strongest possible net force for these two forces? What is the weakest possible net force?...
5 answers
What is the frequency of light having a wavelength of 586 nm? What is the wavelength (in nm) of radiation having a frequency of 7.27 x 109 Hz? (This radiation is in the microwave region.)(a) Frequency of light:X10Hz(Enter your answer in scientific notation)(b) Wavelength of radiation:x10nm(Enter your answer in scientific notation)
What is the frequency of light having a wavelength of 586 nm? What is the wavelength (in nm) of radiation having a frequency of 7.27 x 109 Hz? (This radiation is in the microwave region.) (a) Frequency of light: X10 Hz (Enter your answer in scientific notation) (b) Wavelength of radiation: x10 nm (E...
5 answers
71nf {(r) = f0 Lix} nu sen b f6=) sio(l/rl - WW-lelllr) "zid d !br Jullnng Muat 4nee D (-#,uu(ut)? You Eaeeu Ito jety nh RemarcMiat LC7baautrd(b) cominunox(=) dErraiLl(2) burrowriclr alur purtyNc,dr_ EJunsec} 43atjl) - {:a( cainou nrrnod dnntisr (ctyrboc)
71nf {(r) = f0 Lix} nu sen b f6=) sio(l/rl - WW-lelllr) "zid d !br Jullnng Muat 4nee D (-#,uu(ut)? You Eaeeu Ito jety nh Remarc Miat LC7 baautrd (b) cominunox (=) dErraiLl (2) burrowriclr alur purty Nc,dr_ EJun sec} 43at jl) - {:a( cainou nrrnod dnntisr (ctyrboc)...

-- 0.025730--