4

HW4: Problem 12Previous ProblemProblem ListNext Problempoint) Use implicit differentiation to find the slope of the tangent line to the curve defined by zy8 + 2xy 3...

Question

HW4: Problem 12Previous ProblemProblem ListNext Problempoint) Use implicit differentiation to find the slope of the tangent line to the curve defined by zy8 + 2xy 3 at the point (1,1).The slope of the tangent Iline to the curve at the given point is

HW4: Problem 12 Previous Problem Problem List Next Problem point) Use implicit differentiation to find the slope of the tangent line to the curve defined by zy8 + 2xy 3 at the point (1,1). The slope of the tangent Iline to the curve at the given point is



Answers

In Exercises $29-44,$ solve the given problems by using implicit differentiation. Find the slope of a line tangent to the curve of the implicit function $x y+y^{2}+2=0$ at the point $(-3,1) .$ Use the derivative evaluation feature of a calculator to check your result.

We want to find the slope of the tangent line of the curve, Y equals to co tangent. Yeah. A three X. Where x equals pi over 12. So we see that when we take the derivative of this, end up getting this graph right here. Um And we want to remember that when we take the derivative of the code tangent of X, it's going to be negative Costa Rican X. A negative coast again squared X. So because we get negative Costa Rican spread act, it makes sense that this is the graph that we end up with. So we're going to evaluate this With x equals high over 12. So we see that we end up getting a negative 12, which means that is the slope of our graph. Um at Pi over 12 where F a bex two eagles to co change in three exes are function.

Oh we want to find the slope of the tangent line to the 0.11 on the equation. X cubed plus two X Y plus y squared equals support to solve this problem, we're going to use the process of implicit differentiation which from which we differentiate both sides with respect to X. And solve for dy dx the rate of change of the equation as we listen to steps here. Then we'll find dy dx at that point to find the slope. So first differentiate every term with respect to X in this equation. This gives us D D X X plus two xy xy squared. Because deedee export on the left hand side we take a simple derivative followed by the product rule followed by another simple derivative, unpleasant generalization to obtain three X squared plus two Y plus two X. Dy dx plus two Y. Dy dx on the right hand side seats for the concert and become zero. Next we saw for dy dx. Let's isolate dy dx on one side of the equation. Notice how I made this a little bit simpler here. So do I D X two X plus two Y equals negative three X plus two Y. Or do I d x equals negative three X plus two Y over two X plus two Y. Next to find the slope. We plug in the 20.2. Dy dx +11 equals negative three plus 2/2 plus two. Or negative 5/4.

Okay. This question is asked us to find the slope of the tangent line with this equation at X equals 0.15 And then verify it using the derivative finding function on the calculated. Okay, so we need to take the derivative clearly, we're going to use quotation role. So why prime equals X. The denominator times the derivative of the top. The derivative of the top will be six. Co sign three X. That three popping out in front minus the derivative. The bottom which is one times the original top which is to sign three X. All over the denominator squared. Ok. We don't have to worry about simplifying this down too much because we're substituting a number in here. We're substituting in that 0.15 15 times three will be a 30.45 Make a little bit easier calculations. Okay, substituting in 0.15 Sorry about that everywhere we see an X. Yeah, we're dividing by 0.5 square. Okay, we use that calculator for this number crunching So set up a fraction 0.15 six co sign 0.45 Okay, my ass to sign 0.45 divided by 0.15 squared gives us negative 2646 Oh. This is the slope of the tangent line. We can just check that. Using the derivative. Finding function on a calculator. Okay, on the T I 84 I'll show you where that is. Second. Okay, we're gonna go into math, we're gonna go down here to end the riff. We'll find us a numerical derivative. We're looking for DDX we're gonna put our function in here. We'll set it up as a fraction is to sign three X over X. And we wanted the numerical derivative at 0.15 So we put that in here and there, it confirms it for us. So, slope of the tangent line at that point negative 2.646


Similar Solved Questions

3 answers
10. (15 points) Let S denote the surface determined by < = 22 y? , where 22 + y? < 4 Find the surface area of S. (b) Use Stoke s theorem to evaluatefI curl) . ii dS where F denotes the vector field F = (2+47 _ 1)i+(-r2 +9)j.
10. (15 points) Let S denote the surface determined by < = 22 y? , where 22 + y? < 4 Find the surface area of S. (b) Use Stoke s theorem to evaluate fI curl) . ii dS where F denotes the vector field F = (2+47 _ 1)i+(-r2 +9)j....
3 answers
JuoLed Elencnun CalculinHomework: Section 1.3 Homework sccte: 0 0 1 p 1.3.9 'linjaempleatomA = hi-(Snctn
JuoLed Elencnun Calculin Homework: Section 1.3 Homework sccte: 0 0 1 p 1.3.9 'linjaempleatom A = hi- (Snctn...
5 answers
Hominarar unieimupn ansttrt = {Dlblng Q Qutthon'companIhese AocutCo naaedDavtloo point Estitnete of tne Oroportion Of the stock: decnee)hianetr nting Or5Devclop point esumate of ttic proportion 6f tnc Korningsto} decmals) ~Develop point estmate cftha proportion oftre Hornmnaster stoc-5 ~dramalso4 Wer Teepd ancrsAte TalcoSurs
Hominarar unieimupn ansttrt = {Dlblng Q Qutthon' compan Ihese Aocut Co naaed Davtloo point Estitnete of tne Oroportion Of the stock: decnee) hianetr nting Or5 Devclop point esumate of ttic proportion 6f tnc Korningsto} decmals) ~Develop point estmate cftha proportion oftre Hornmnaster stoc-5 ...
5 answers
A person' weight W varies inversely as the _nd power of the distance d from the center of a planet: A person weighs 240 pounds at a distance of 1000 miles from the center of the planet Betta-Z. How much does the same person weigh at a distance of 4000 miles from the center of the planet? Show work, including finding the value of kOk = 360 X 2000, weight3600 poundsOk = 360 X 20002 weight90 poundsOk = 2, weight480 poundsNone of the above is correct
A person' weight W varies inversely as the _nd power of the distance d from the center of a planet: A person weighs 240 pounds at a distance of 1000 miles from the center of the planet Betta-Z. How much does the same person weigh at a distance of 4000 miles from the center of the planet? Show w...
5 answers
4 +26(10 pts:) Let W be the st of all vectors of tbe form Wa subspace o R'? ExplainW Or why not .
4 +26 (10 pts:) Let W be the st of all vectors of tbe form Wa subspace o R'? Explain W Or why not ....
5 answers
Whether cach of the fol- Usc thc Comparison Test or Limit Comparison Test to dcterminc lowing series converge Or diverge3n _ 20++1 n' +n?44
whether cach of the fol- Usc thc Comparison Test or Limit Comparison Test to dcterminc lowing series converge Or diverge 3n _ 2 0++1 n' +n? 44...
5 answers
Given fuuction f R define D; € R to be the set of points where the function f fails t0 be continous: [n Section A. WC SaW that Diriehlet' $ function g(r) had Dg The modlilication h(r) of Dirichlet'$ funetion had Dh RA{0}. LCTo being the only point of continuity. Finally: for Thonae $ funetion t(). wC Saw that DtExercise 4.6.1 Using modifications of these functions, construct [uction f : R +Rs thatDf = %'
Given fuuction f R define D; € R to be the set of points where the function f fails t0 be continous: [n Section A. WC SaW that Diriehlet' $ function g(r) had Dg The modlilication h(r) of Dirichlet'$ funetion had Dh RA{0}. LCTo being the only point of continuity. Finally: for Thonae $...
5 answers
Points) Suppose that thc total revenue function for product 1s R(x) 500x 21" dollans that thc total cost funetion is C(x) 3600 100x 2x? dollars . In both cases,X is tie number of units.Find the prolit function P(x) and use It to find thc profit from the production and sale of 100 unlisFind the marginal protit function;Find the marginal prolit when [00 units are sold, Interpret your result like we did in class.
points) Suppose that thc total revenue function for product 1s R(x) 500x 21" dollans that thc total cost funetion is C(x) 3600 100x 2x? dollars . In both cases,X is tie number of units. Find the prolit function P(x) and use It to find thc profit from the production and sale of 100 unlis Find th...
1 answers
Write the system of equations corresponding to each augmented matrix. $\left[\begin{array}{rrr|r}1 & 3 & 2 & 4 \\ 2 & 0 & 0 & 5 \\ 3 & -3 & 2 & 6\end{array}\right]$
Write the system of equations corresponding to each augmented matrix. $\left[\begin{array}{rrr|r}1 & 3 & 2 & 4 \\ 2 & 0 & 0 & 5 \\ 3 & -3 & 2 & 6\end{array}\right]$...
5 answers
Find the derivative of f with respect to x of f(x) = In x4 . The derivative of fwith respect to X of f(x) = In x4 isand then click Check Ansu
Find the derivative of f with respect to x of f(x) = In x4 . The derivative of fwith respect to X of f(x) = In x4 is and then click Check Ansu...
5 answers
What is the tangent plane equation of sphere f(ry :)-r+y+?=6 at Point (1,1.2) ?2r+4y-T-+ll-0~-J+2+4=0X-J-2-+2=0r+2y-:+6=03r + 2y--/2+9=0
What is the tangent plane equation of sphere f(ry :)-r+y+?=6 at Point (1,1.2) ? 2r+4y-T-+ll-0 ~-J+2+4=0 X-J-2-+2=0 r+2y-:+6=0 3r + 2y--/2+9=0...
5 answers
1. [15 points] Continuous random variable X has the following probability density function (PDF):2x, 0 <x <1 fx(x) = {2, otherwiseFind the cumulative distribution finction (CDF) Fx(x)_ b) Determine the expected value E[X] and variance Var[X]:
1. [15 points] Continuous random variable X has the following probability density function (PDF): 2x, 0 <x <1 fx(x) = {2, otherwise Find the cumulative distribution finction (CDF) Fx(x)_ b) Determine the expected value E[X] and variance Var[X]:...
5 answers
TraceA and P-IAP have the same traceCharacteristic polynomialA and P-IAP have the same characteristic polynomial_EigenvaluesA and P-IAP have the same eigenvaluesEigenspace dimensionIf A is an eigenvalue of A (and hence of P-IAP) then the eigenspace of A corresponding to A and the eigenspace of P-!AP corresponding to A have the same dimension.
Trace A and P-IAP have the same trace Characteristic polynomial A and P-IAP have the same characteristic polynomial_ Eigenvalues A and P-IAP have the same eigenvalues Eigenspace dimension If A is an eigenvalue of A (and hence of P-IAP) then the eigenspace of A corresponding to A and the eigenspace o...
5 answers
Given that the length of a certain brand of pencil has a normaldistribution with6=μinches and5.0=σinches, find the probabilitythat a randomly chosen pencil will have a length between 5.5 inchesand 6.25 inches.
Given that the length of a certain brand of pencil has a normal distribution with6=μinches and5.0=σinches, find the probability that a randomly chosen pencil will have a length between 5.5 inches and 6.25 inches....
5 answers
617 + 8x T _= 13 =3 212Ix 81 Ix=2 =2Tx + 82 + 13 Ix + 212 + 8x Ix + 312 13solution:(21,32,*3) = (4,2,-1) (31,12,*3) = (~1,0,3)
617 + 8x T _= 13 =3 212 Ix 81 Ix =2 =2 Tx + 82 + 13 Ix + 212 + 8x Ix + 312 13 solution: (21,32,*3) = (4,2,-1) (31,12,*3) = (~1,0,3)...
5 answers
(etictr)3p1#r)(2 _Tefuntion flc)dcfnedforedocsnoi havz . limit at = aifaGuasion3 ptsfor > < 5 is continuous Ifc =_ for $ > 5The tunction f(~) =
(etictr) 3p1 #r)(2 _ Tefuntion flc) dcfnedfore docsnoi havz . limit at = aifa Guasion 3 pts for > < 5 is continuous Ifc =_ for $ > 5 The tunction f(~) =...
5 answers
Find the missing libuisn the Quadrant fact that P lies on the unit circle 8 given quadrant:
Find the missing li buisn the Quadrant fact that P lies on the unit circle 8 given quadrant:...
5 answers
Find all values of & for which all solutions of 2y" +axy + (5/2)y = 0 approach zero as € - 0.
Find all values of & for which all solutions of 2y" +axy + (5/2)y = 0 approach zero as € - 0....
5 answers
Consider a particle of mass m moving in the region x > 0 under the influence of the potentialU(x) = Uo(+3where Uo = 1 J and a = 2 m_Sketch the potential, find the equilibrium point(s) and determine whether they are maxima Or minima. (bZ Determine whether the particle can escape from the potential with a finite escape velocity at x = a. Ifit is impossible, explain why not:
Consider a particle of mass m moving in the region x > 0 under the influence of the potential U(x) = Uo (+3 where Uo = 1 J and a = 2 m_ Sketch the potential, find the equilibrium point(s) and determine whether they are maxima Or minima. (bZ Determine whether the particle can escape from the poten...

-- 0.069448--