5

2 consider the function: 9(2) Vr Use the defnltion of derivative (limits) to find 9' (3) baeind (herequation of the tangent line to the curve y = 9(r) atthe po...

Question

2 consider the function: 9(2) Vr Use the defnltion of derivative (limits) to find 9' (3) baeind (herequation of the tangent line to the curve y = 9(r) atthe point I = 3. Graihimecurve of the function and the tangent line to the curve at I on the same set of axes NoresHYourav draw the graph by hand and upload Hsoluse pholo embedded In the = camputer t0 draw the one file vou are 'uploading You map Eubelor graphs Your Rraph) must be part of the orie file YOu upload for this MMAreGiteria:

2 consider the function: 9(2) Vr Use the defnltion of derivative (limits) to find 9' (3) baeind (herequation of the tangent line to the curve y = 9(r) atthe point I = 3. Graihimecurve of the function and the tangent line to the curve at I on the same set of axes NoresHYourav draw the graph by hand and upload Hsoluse pholo embedded In the = camputer t0 draw the one file vou are 'uploading You map Eubelor graphs Your Rraph) must be part of the orie file YOu upload for this MMAreGiteria: straight axes, axes labelfed arid project See the Eohla place scaled; smooth curve; straight Langent line: tangent line Jamei



Answers

$9-10$ Sketch a direction field for the differential equation. Then
use it to sketch three solution curves.
$$y^{\prime}=\frac{1}{2} y$$

So we have the Parametric Equations X is equal to two t. Why is important to t cute? And we want to look at the point where cheese equipped with one. So for first part, we want to find an expression for the derivative. So we start with the expired ET, which is equal to two and then d y by D. T, which is equal to three. T squared. So we can now go ahead and find the expression for the bye bye T x d by Buddy X will be called to D y e t, divided by D X by TT so that's equal to three. T squared over two. So there's my expression for the derivative. Now for part me, I need to actually find the values to derivative vertical to one so I can say a physical 21 d y by D. X is equal to 3/2. Also, X will be equal to two, and why will be equal to one? So we have our point to one, and you have the slope which is equal to 3/2. So the change into the curve at the point to one is a line off slope to your to which both to the point to one. So the purple line here is the key aged line and the green curve here is the cover presented by X equal to two. T y is equal to take it.

The permit questions that we have. X incredulity duty by Nico June The T bird three entity e could humanise one from the first equation confronted the X over DT equals to and similarly that do I already d included a treaty square. Now it will be valued and the take a humanist one Get echo cheated three From here we can find a d Why? On my deep Thanks we could you know, Do you want over the day your funding, Buddy X mama d d And then we get ico June uh, three d of anybody do. So this will be the slump am here Now we record attention, like question would be why Coach and X plus B and they were given the Amarante. So again, if I treat you experts be to find it be noticed. And that thing could you minus one. We get a bone for the X one will be one to minus one. Therefore doesn't implies that minus one coach in that tree out of two times honest to be And if I don't get it doesn't means that be we could do a dreamless one with two on we're gonna tend to line will be under form. Why could directory and about you express to

I'm an examination today will be solving this problem. So first we have to take the implicit differentiation of dysfunction so we can start off by taking the dura tive of Excess square, which is two x time July Square course. That's a squared times, too. Why times D y over DX. This is known as a product rule because there's you're your most playing at the Square times Y squared it. When you have a multiplication like this between two variables, you have to use it. Part of cruel right here has shown and is equal to zero. And so we have to separate just D y over DX by itself. We can do that by subtracting two eggs times y squared on both sides and then dividing it by X squared times to Y on both sides. So once we subtract two, it's times y squared will get invited to eggs times y square. And then we divide X squared times to wear but both sides so you get a D Y over D. X is equal to negative to X Y squared over two X squared. Why? And you could cancel out the twos and you could also cancel out some of the X and y very well. So you can cancel ex. You could cancel out the squared. It gets a lot to square the y and cancel out the white term on the bottom. So just be Do I over DX is equal to negative? Why over X To find the tangent line at this point, you have to plug in this point into the differentiated ah equation. So we'll just be do you? Why? Over DX is equal to negative three over negative one, which is equal to three. You do this so that you could determine the slopes O D Y o r d x uh, At this point, once you plug in the numbers of this point into D i. D. X represents the slope so you can represent the tension line by writing Why is equal to three x close Be and you have to solve be by Pauline this point again into this function. So beat three is equal to three times negative one plus B. So we three is equal to negative. Three must be and be well equal to six. So the tangent line is why's equal to three x plus six. And so this is the tangent line. Um, at this point in this function, So So there's the 10 right? And to find the normal and the Noland is just the perpendicular line two, the tangent line at this point, so you can determine that. Uh, bye. If you know, um, the slope of a tangent line, you should know that, uh, it is the negative reciprocal off. If you want to know the slope of the normal in my bed. If you want to know the slope of the normal line, you have to take the, um, negative reciprocal of the slope of the town in mind. So it would just be negative one over three. Thanks. Because be and so you plug in the same point cause you're trying to find normal line at that point. So just be three is equal to negative one over three times negative one plus. So once you saw this, you you have to multiply changes into a fraction s so that it's nine over three so that you could carry this term to this side. So is equal to one over three post being. So once you if he's attract negative. If you subtract one or three on both sides, you get easy, but to eight over three. And so the equation in the normal and his wise equal to negative one over three eggs, plus a over three and to make it much more easier to understand, um, the dysfunction or this line we have, we can just move by everything by three. So it's just three. Why is equal to Negative X Plus eight or a confusion as three? Why is equal to a minus X? So this is the equation of the normal line at that point at at negative one common three. I hope this hope thank you.

We've got the equation. X squared y squared equals nine and we're working with the point. Negative 13 First, they wanted us to verify that that point is on the graph Negative. One squared is one three squared is 91 times three is not so That's her easy shot. Now they want us to find the equation of the Tanja line and the normal line at that point with the first derivative will give us the equation of the Tangela. So I want to find the first derivative of this using implicit differentiation. So that means that we will have to use the product rule here. First function X squared times the driven About second Which will be to Why Times? D y d X or just y prime. Plus the second function the Y squared times The derivative of the first function Drood off two x of X squared is two X and that will equal the derivative of nine. And the derivative of any constant is zero. So now I can solve this for why prime? If I want to, uh, let me just double check the other directions. Didn't say anything about giving the equation of my first your evidence. So the probably the easiest thing to do would just be right now plug in the negative one of the three and solve it for why Prime? So X negative one squared. Why is 32 times three? So that's gonna give me six y prime. Why Squared is nine times two times negative. One is negative. Two that'll give me minus 18 equals zero. So that means six y prime equals 18 which means why Prime equals three. So that's this hope of my tangent line so we can find the equation of the Tanja line if we wanted in soap intercept form just by plugging in my three for the why and my three for the slope and the negative one for the X and then possum be and figure out the lie intercept. So three equals negative three plus B. So that means six equals B. So there's my Y intercept. So that means the tangent line will be Why equals three X plus six now for the normal line that's perpendicular to the tanja line. So that means the soap will be the negative reciprocal of three. So my why corn it's still three, but now my slope is negative. 1/3 times negative one plus B. So three equals 1/3 plus B and then we subtract the 1/3 from both sides, and I'm going to switch this to an improper fraction. So my y intercept his 8/3 so the normal line will be. Why equals negative 1/3 x plus 8/3.


Similar Solved Questions

5 answers
(c) 198x J8s 1.2388 10* m $ What is the resistivity of gold J 4 temperature of 65*C? (a) 2.813 * 10-* { m (b) 2.067 x 10-* Q m (c) 2.194 * 10-" _ Q m (d) 1.963 * 10-* 0 m
(c) 198x J8s 1.2388 10* m $ What is the resistivity of gold J 4 temperature of 65*C? (a) 2.813 * 10-* { m (b) 2.067 x 10-* Q m (c) 2.194 * 10-" _ Q m (d) 1.963 * 10-* 0 m...
5 answers
Which one of the following atoms has the largest radius? 4)0 B) F C) $ D) CI
Which one of the following atoms has the largest radius? 4)0 B) F C) $ D) CI...
5 answers
Calculate the three significant figures the rms (Vrms), average (v), and most probable speeds (Vm) of helium gas molecules at 300 k ,and the number of representative points per unit volume within the shell or the density pv in the most probable speed (Vm): where mh =6.7 *10-27 kg and h=6.6*-34j ,K8 =1.38*10-23 jlk and NA =6.07*1023.
Calculate the three significant figures the rms (Vrms), average (v), and most probable speeds (Vm) of helium gas molecules at 300 k ,and the number of representative points per unit volume within the shell or the density pv in the most probable speed (Vm): where mh =6.7 *10-27 kg and h=6.6*-34j ,K8 ...
5 answers
What is the vclue & ftx) tan x Sec*x Over fhe intecva / Zo, 4]?
What is the vclue & ftx) tan x Sec*x Over fhe intecva / Zo, 4]?...
5 answers
Summarize the pertinent information oblained by applying the graphing strategy &nd sketch the graph ofy=f6x} f(x) = (x- 3)(*2 6x - 18)
Summarize the pertinent information oblained by applying the graphing strategy &nd sketch the graph ofy=f6x} f(x) = (x- 3)(*2 6x - 18)...
5 answers
Mo Q) A rocket of mass 1.4 x 105 kg 75% of which is fuel is launched from JV:Ue' space station On the earth surface to the deep space where there are no appreciable external forces. "(neglecting the earth rotation) a) Ifthe exhaust speed is 4.8 km/s, what is the speed of the rocket when the fuel has been burned b) Ifthe burning fuel requires 600 sec, wlat is thc force exented by the engine ofthe rocket
mo Q) A rocket of mass 1.4 x 105 kg 75% of which is fuel is launched from JV:Ue' space station On the earth surface to the deep space where there are no appreciable external forces. "(neglecting the earth rotation) a) Ifthe exhaust speed is 4.8 km/s, what is the speed of the rocket when th...
5 answers
Charcoal is primarily carbon. Determine the mass of $mathrm{CO}_{2}$ produced by burning enough carbon (in the form of charcoal) to produce $5.00 imes 10^{2} mathrm{~kJ}$ of heat.$$mathrm{C}(s)+mathrm{O}_{2}(g) longrightarrow mathrm{CO}_{2}(g) quad Delta H_{mathrm{rxn}}^{circ}=-393.5 mathrm{~kJ}$$
Charcoal is primarily carbon. Determine the mass of $mathrm{CO}_{2}$ produced by burning enough carbon (in the form of charcoal) to produce $5.00 imes 10^{2} mathrm{~kJ}$ of heat. $$ mathrm{C}(s)+mathrm{O}_{2}(g) longrightarrow mathrm{CO}_{2}(g) quad Delta H_{mathrm{rxn}}^{circ}=-393.5 mathrm{~kJ} ...
1 answers
Compute $x(0.1)$ by solving the differential equation $$ \left\{\begin{array}{l} x^{\prime}=-t x^{2} \\ x(0)=2 \end{array}\right. $$ with one step of the Taylor-series method of order 2 (Use a calculator.)
Compute $x(0.1)$ by solving the differential equation $$ \left\{\begin{array}{l} x^{\prime}=-t x^{2} \\ x(0)=2 \end{array}\right. $$ with one step of the Taylor-series method of order 2 (Use a calculator.)...
5 answers
Placed 20 3 cm bofore diverging lens of focal length -30 converging lens ol focal lenglh 16 0 cm is placed 15,1 cm An abjed aner the Iirgl Ions Whal is Ie distance ofthe fnal image hom tho second lens? (Stale answer cenlimelers with digit right of decimal Use negalve sign Winage is belore sacond Ions
placed 20 3 cm bofore diverging lens of focal length -30 converging lens ol focal lenglh 16 0 cm is placed 15,1 cm An abjed aner the Iirgl Ions Whal is Ie distance ofthe fnal image hom tho second lens? (Stale answer cenlimelers with digit right of decimal Use negalve sign Winage is belore sacond Ion...
1 answers
Suggest syntheses for each of the following from $\quad \mathrm{K}^{15} \mathrm{NO}_{3}$ (a) $\quad \mathrm{Na}^{15} \mathrm{NH}_{2}$ (b) $^{15} \mathrm{N}_{2}$ and (c) $\left[^{15} \mathrm{NO}\right]\left[\mathrm{AlCl}_{4}\right]$
Suggest syntheses for each of the following from $\quad \mathrm{K}^{15} \mathrm{NO}_{3}$ (a) $\quad \mathrm{Na}^{15} \mathrm{NH}_{2}$ (b) $^{15} \mathrm{N}_{2}$ and (c) $\left[^{15} \mathrm{NO}\right]\left[\mathrm{AlCl}_{4}\right]$...
5 answers
According Journal arde on ancicnt Japanese history; every samural became masteress (ronin) during the feudal %gr atjapan hisloqtun randomly and independenty selected 20 samurai that served during the teudal period and & curiols wfiethcr [nty becae ronins 31 ToiT pointsin thalr lives_What is the probability that at least 5 were ronins some polnt In thetr Ing? 10.8040.3700.196D 0.630BecLSeleqop
According Journal arde on ancicnt Japanese history; every samural became masteress (ronin) during the feudal %gr atjapan hisloqtun randomly and independenty selected 20 samurai that served during the teudal period and & curiols wfiethcr [nty becae ronins 31 ToiT pointsin thalr lives_What is the ...
5 answers
Q1. Draw all possible E1 products of the reaction of2-bromo-2,3,4-trimethylpentane with methanol(consider thepossibility of rearrangements on the carbocation)Q2. Show all conditions it would need to produce the cinnarizinevia an SN1 reaction. Draw the mechanisms.benzhydryl chloride+1-trans-cinnamyl-piperazine -->cinnarizine(drug)
Q1. Draw all possible E1 products of the reaction of 2-bromo-2,3,4-trimethylpentane with methanol(consider the possibility of rearrangements on the carbocation) Q2. Show all conditions it would need to produce the cinnarizine via an SN1 reaction. Draw the mechanisms. benzhydryl chloride+1-trans-cinn...
5 answers
The formula 5= C(1 +r}" mode inllabion; where valme tonay the annua inrarion rale: (in decimal form) ine intlaled valle Vean? rom no Ue infation rare hovi Miich will a house no"worn $104, OOC Ee wiorth in ?1 years? Round youI answver ncates: dollarhousu vall be worth(Round the nearesl uollzneeded;"
The formula 5= C(1 +r}" mode inllabion; where valme tonay the annua inrarion rale: (in decimal form) ine intlaled valle Vean? rom no Ue infation rare hovi Miich will a house no"worn $104, OOC Ee wiorth in ?1 years? Round youI answver ncates: dollar housu vall be worth (Round the nearesl uo...
5 answers
10_ FIND the #lowing iregral:sin & + ^an &11, Find %he Ictal EXACT ucu ofske scicd region erelosd by Ikx (llwing giver: cerves. sin 2 $ Ed 0t (srs#)
10_ FIND the #lowing iregral: sin & + ^an & 11, Find %he Ictal EXACT ucu ofske scicd region erelosd by Ikx (llwing giver: cerves. sin 2 $ Ed 0t (srs#)...
5 answers
Points Save Answerpressure of the earth's atmosphere Is 7.2 Iblin?, What Is the pressure when expressed in kg/m27(2.54 cm = in,, 2.205 Ib = 1kg)1.03x104 kg / m2
points Save Answer pressure of the earth's atmosphere Is 7.2 Iblin?, What Is the pressure when expressed in kg/m27(2.54 cm = in,, 2.205 Ib = 1kg) 1.03x104 kg / m2...

-- 0.020132--