3. f(x) = -x² +1 Ex)(+x). x2 + x - 6 %3D Holes: Vert. Asy: Hor. Asy:

Q: For what value yo does the initial value problem y = Vy² – 9 with y(xo) = yo have a unique solution…

A: In this question, we have to use the uniqueness theorem and find the appropriate values of y0

Q: The integrating factor of the LDE y' = x - 2ycotx is

A:

Q: Solve the differendialegimaition: (2x+e)dx + (xay co

A: Make some simplification and rearrange the given differential in exact form.

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: Z=8x+12y subject to 4x+6y>14 , 4x+5y > 9, x20, y20 x=? (2 decimal places) Minimize

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Q: The third iteration, when the positive x-intercept of y=f(x) is approximated via the Interval…

A: The root of a function can be calculated using a numerical method. The value of the function is…

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: Find the general solution of the DE y’’ = xsin(x)

A: Topic = Differential equation

Q: 7. what is the durivative oF q= arc cSc V1-3X %3D 3 Cz -Gx)I- 7 X 3. C2-6x)1-3x (-3x)-3x 3 C1- 3x)-3

A: First make it in simple trigonometric functions then diffrenciate it and just put all the given…

Q: 2Use divectional devivative delinihion of f(Hiy)=x y'at the divecionof ū =i jatthe Point (le2>

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

A:

Q: f(x)=x²-2x Sf(x)dx using four subintervals by on Estimate -1 d M4.

A: Given function is We divide the interval [-1,1] into four sub-intervals with length of each is…

Q: Determine the value of the Wronskian W(y1, y2) of y" - 2y + 1 = e2*(x + 1) if x-0.2 by using…

A: Given, y''-2y'+1=e2xx+1. The objective of the problem is to obtain the value of the Wronskian if…

Q: (4) The general solution to 7xy" – y + 10y = 0 is y = Ax x + x+ +В х + x+ x²+ x³ + and converges on…

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Q: Obtain the General Solution (x-1 )dx - (3 x -2y -S) dy = 0 MAM

A:

Q: Given that y' = 2x + x²y, where y(0) = -1 with step size h=0.1. Estimate the values of y(0.2) using…

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Q: What is the minimum value of y = 3 + cos 2x?

A: Please go through the attached solution. I hope that this solution will help you. Thankyou . Best…

Q: 3. Find the interval on which the curve of y= 2 1+3t+t² dt is concave up.

A: Second derivative is positive.

Q: What happens when you try to approximate V3 by using fixed point iteration of g(x) = 3/x?

A: To determine what happens when 3 is approximated using fixed-point iteration.

Q: Solve the given optimization problem by using substitution. Minimize S- xy + xz + yz subject to xyz…

A: S=xy+xz+yz  =xyzz+xyzy+xyzx

Q: Determine the value of the Wronskian W (y1, Y2) of y" – 2y +1 = e2 (x +1) if x=1.3 by using…

A:

Q: The

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

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

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Q: e largest interval in wh

A: In this question, the concept of Interval of Unique solution is applied. Given, the Differential…

Q: Find the root of f(x)=(x-4){(x+2)= 0, using the initial guesses of x, =-2.5 and Xy = -1.0, and a…

A:

Q: - Use Euler's method to estimate y(3) given y(0) = 1, and y' = x -. Use steps of h = 1

A: use euler method for finding the y(3)

Q: et Xi- Nco,1) and n=2 T=X,+Xz Show that Tis Sufficiencs y Statistic

A:

Q: Consider the initial - value problem y' --2x, y(1)-2. Show that Taylor's method of order 2 ives the…

A:

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

A:

Q: 4. Find a particular solution of y" + y' = cost cos 2t cos 3t.

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

Q: Solve the following boundary value problem using finite difference method. y." = y1 Or, y:' = y2 y2'…

A:

Q: Solve the initial value problems for y as a functionof x. (x2 + 1)2 dy/dx = √x2 + 1, y(0) = 1

A: x2+12dydx=x2+1⇒dydx=x2+1x2+12⇒dydx=1x2+132⇒dy=1x2+132 dx Now integrating on both sides, we get…

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: (2)If ø = xyz – 2 y²z+x²z?. Find div grad ø at points (2,4,1)

A: Given that        Φ =xyz-2y2z+x2z2  Here we have to find div grad Φ at points (2,4,1).

Q: Obtain a numerical solution of 2y + y - x=0 using Euler's method with step size equal to (0.5) and…

A:

Q: For the cost function C(x)=300+10x+0.03x^2, show that average costs are minimized at the x value…

A: Given data: The expression for the cost function is C(x)=300+10x+0.03x2.   The expression for the…

Q: 2. Evaluate f(x) = e3x + 2 at x = -1. Round to the nearest thousandth. %3D %3D f(-1) = ...

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

A:

Q: A- solve = x + y² with condition y (0) = 1, x o= 0 to x =0.2 and h = 0. by Rung kutta dx method 4th

A: The given differential equation is dydx=x+y2 with conditions y0=1, x0=0 to x=0.2 and h=0.1.

Q: II z= ě Y x - Juv Find dz dv üs ing chein rule.

A:

Q: In(|(2 +1)"(z + 3)|l) 15x - 13 dx = X (Don't forget to include the constant of 2-2x 3…

A: topic - indefinite integral

Q: Find the Bolution to the initial value problem. | -y = 2€ %3D %3D

A: Given IVPy'''-y'=2e-t+9e2t  ; y(0)=0 ,  y'(0)=-1   , y"(0)=2 to find the the general solution use…

Q: Solve the initial-value problem for yy as a function of xx. (64−x2)dydx=1,y(0)=5(64-x2)dydx=1,y(0)=5

A: (64-x2)dydx=1⇒dy=dx64-x2integrating,                ∫dy=∫dx64-x2+c      [c=…

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

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Q: Find the solution of the initial value problem substitution y-erX in to given defind

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Q: 9. y = Arccot“ Vx 2 Arccot Vx А. Arccot x С. Vx(1+x) x' +x* Arccot x В. Arccot x Vx(1-x) D. - -…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3.Please resubmit the question and…

Q: Consider the initial value problem {y′−3y=6, {y(0)=1. What is the limit of y(x) as x approaches −∞?

A: