2. Show that g(x)= *** has a unique fixed point in [0,1] and find an approximation to the point that is accurate to within s=10.

Q: 4. Find the orthogonal trajectories of the given family of curves. y = cx'.

A: Solution:-              y=cx3 →          1              Diff. w.r.t x            ⇒dydx=3cx2…

Q: find a linearization at a suitably chosen integernear a at which the given function and its…

A: Given that the function is  f(x)= e-x, a= -0.1 To determine the linearization for the function.  The…

Q: 3. Find the maximum and minimum values of a 1 āz - on |z| ≤ 1 (where a with la| < 1 is fixed)

A:

Q: 7-The tangent of the curve x^2+y^2- 2xy3D0 at the point (1,1), is * O a. y=2-x. O b. y=x-2. C.…

A: We find equation of tangent to the curve

Q: Suppose f(x, y) = x² + y² – 2x – 8y +1 (A) How many critical points does f have in R? ? (B) If there…

A:

Q: (d) Finally, show that the conditions for the theorem are not satisfied for the initial value…

A: (D) here fx,y=y13 differentiate it with respect to x ∂f∂x=13y-13dydx initial condition y0=0

Q: Use Euler's Method to approximate a y(x) solution to the initial value problem [image] at points:…

A:

Q: (1) Use the linear approximation of Va at x = 9 to estimate the value of v8.7

A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the other…

Q: Suppose that T is to be found from the formula T=y( e*+ e-X), where x and y are found to be In 5 and…

A: GivenT = y(ex + e-x)

Q: 3. Find for the simplified general solution of (1 + x³)dy - x²ydx = 0

A:

Q: Solve the following initial value problem over the interval fromt= 0 to 2 where y(0) = 1. Display…

A:

Q: Solve the initial-value problem for y as a function of x. (16 – x)- dy = 1, y(0) = 5 dx ((1 - D- -…

A:

Q: 4. Determine the maximum point of the the graph of y = 12 sin(π – 2x), for x = [-T, T).

A: Given:         y=1-2sinπ-2x     To get the maximum value of the function the derivative is equal…

Q: Q11 Determine all the critical points for the following- S(x) = sin'x- cosx On the interval (0, 2n).

A: Given , f (x) = sin2x - cos x  (.) Definition :  Then critical point of a…

Q: We have found the following Wronskians. W = −e-³x; W₁ = −e-²x (4 + ex)-¹; W₂ = e¯x(4+ e*)-¹ Р We…

A: NOTE: Refresh your page if you can't see any equations. . here we have

Q: 1) Approximate the value of y for 0sxs1.5 using the Euler method if the step length is h=0.5.

A:

Q: 4 Find the linearization of the function f (x) = x² at x = 1. L(x) = Using this linearlization, ƒ…

A: f(x)=x4 at x=1 So, L(x)=f'(1)(x-1)+f(1)

Q: 15. If g(x) and h(x) are both antiderivatives of some func- tion f(x), then what can you say about…

A: Consider that gx and hx are both antiderivative of function fx. Find gx-hx.   Since gx and hx are…

Q: (6)Find the orthogonal trajectories for the given families of curves 2x2 – 3y = K. Where K is a…

A: We have to find out the orthogonal families of given function Given function   2x2 -3y=K  ;    where…

Q: 11. f(x) = x² + 7x + 10 Opens up/down: Vertex: Axis of symmetry: Solution(s): y-int:

A:

Q: 7  please answer, type the solution if you can please. or write clearly

A:

Q: Sketch the graph of the inhomogeneous term and find the solution to the initial value problem: +…

A:

Q: Consider the IVP: x" +3(x')2 + 10tx = 0, x(0) = - 3, x'(0) = 2 Using the Euler method with a time…

A: Given x''+3x'2+10tx=0, x0=-3, x'0=2, ∆t=0.5

Q: Find the linearization L(x) of y = e5* In(x) at a = 1. L(x) =

A: Given that:y=e5xln(x)a=1To find the linearization

Q: 2 35) Find a curve through the point (-4, 1) whose length integral, 1 s y s 2, is L = 1 +

A:

Q: Suppose that T is to be found from the formula T = x (ey + e-y), where x and y are found to be 2 and…

A:

Q: In x 2. Use a local linear approximation of f(x) = 1+x² to estimate In (0.9) 1.81

A: Given - fx=lnx1+x2 To estimate ln0.91.81 using a local linear approximation of fx. Here we will use…

Q: ii. Establish the stability estimate for the solution of the problem "() - by(le) + ay(t) + f(4) on…

A: Given that , y''t=byt+ayt+fty''t=abyt+ft Therefore the differential equation , y''t-ab yt-ft=0 The…

Q: 1. Find the orthogonal trajectories of the given family of curves: Circles through the origin with…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: The

A: Below is sketch of  the given function.    Rotation about x axis will give a volume in 3D plane.

Q: 5) Construct a linear approximation of the function f(x ) = lacX+s) about the point x,= 1. Compare…

A: Tangent line approximation or linear approximation is very significant in differential calculus.…

Q: nake/s the DE nonlinear y' =1-xy+ y2

A:

Q: 5. Find all the critical points of x + 2 cos x for 0<x<n, and identify each as a local minimum,…

A:

Q: In an effort to make the distribution of income more nearly equal, the government of a country…

A: Given: Lorenz curve for first year: y = 0.97x2.1 And for the next year: y = 0.35x2 + 0.65.

Q: Apply Euler's method with successively smaller step sizes on the interval [0, 2] to verify…

A:

Q: 27. Find the length of the curve Vcos 2t dt y = from x = 0 to x = "/4.

A: The given curve is We know that by Second Fundamental theorem of calculus ,if F(x) is continuous on…

Q: 1. Eliminate the arbitrary constants on the given equation: y = A + Be*

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 12. If z = 2xy – 3x²y and x is increasing at 2 cm/s, determine at what rate y must be changing in…

A:

Q: What is the initial condition at x = 0 of the solution plotted graph c)? on

A: From the given graph, it can be concluded that y = 1 at x = 0 (where graph crosses y-axis).

Q: Solve the following initial value problem over the interval fromt= 0 to 2 where y(0) = 1. Display…

A:

Q: Find X1 & X2 using Newton's method to minimize x2 – y2/2 starting from (1,1)

A:

Q: If f(x) > g(x) >0 for X in [1,0) and g(x) dx diverges to +0, then | F(x)dx also diverges to +. True…

A: It is TRUE, that 0&lt;g(x)≤f(x) for x in [1,∞)  and                               ∫1∞g(x)dx diverges…

Q: If X has hazard rate function Ax(t), compute the hazard rate function of aX where a is a positive…

A: 8) We know that if F(x) is the cumulative distribution function of random variable X  Than…

Q: 5) a) Compute Ko for the function f0=V+X by using the de finition of the deniratire, b) Find the…

A:

Q: Show mathematically that MRS is increasing for U=1-ex +e2y and is diminishing for U=lnX +LnY

A:

Q: 2. The Lorenz curve of a particular society is given by L(x) = Ax? + Bx. %3D Suppose that the…

A: We will use given values in Lorenz curve and Gini index to create equations for A and B , Then solve…

Q: 1 Given f(x)=³-57² +24r, which of the critical number found in the previous number is f(c) a…

A: You must have an idea about to how to find relative maximum or minimum using critical points.

Q: If Newton's method is used to find the critical number of f(x) = a® – a³ + æ² – 2x with initial…

A: Image is attached with detailed solution.

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.