Rewrite c(x) = (x ^ 2 + 5x + 2)/(x - 3) in the form y = q(x) + (r(x))/(b(x)) has degree less than b.

Q: Find the critical number for y = f(x) = x (x + 2)²

A: NOTE: Refresh your page if you can't see any equations. . the given function is take derivative…

Q: Estimate the root of following nonlinear equation x – 2x – 1 = 0 using Newton-Raphson method…

A: (a) The given equation is f(x)=x4-2x-1=0 find the derivative f'=4x3-2 initial guess x0=-1…

Q: I don't understand how the Wronskian method is being applied.

A: Wronskian is a method by which in a differential equation we check the solution of the differential…

Q: = x2 - 4x + 1 with domain [0, 3] f has ---Select--- v at (x, y) = f has ---Select--- v at (x, y) = f…

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Q: Find the perticular number or orthogonal trajectories of x2+cy2=1 passing through the point (2,1)

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Q: Fina aly for y = 3x V3-x4

A: we have to find dy for given y

Q: Is it possible to get a example which shows this applied to a model

A: To determine: An example which shows the application of Taylor series in a model.

Q: Find the domain and all critical points in the domain y=ln(x-5)

A: Domain: (5,∞),{x|x>5}

Q: A number of the form iy is called pure imaginary

A: A number of the form z = x + iy is known as complex number, where x is real part and y is imaginary…

Q: Find the critical numbers of the function.   f(x)  = 2x3 + x2 + 2x

A: We find the first derivative using the power rule

Q: Find the local minima/maxima of -x + ln x if it exist

A: fx=-x+lnx Differentiating with respect to x, we get f'x=-1+1x Now to find critical values, solve the…

Q: Find the critical numbers of f(x) = ln(x2 + 5x + 14).

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Q: evaluate using the appropriate method or combination of methods.

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Q: solve e^-x=lnx using bisection method.

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Q: giver yn f(५) ५) -2x + 3, + 2, find of ax

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Q: Find the explicit solution of the separable equation

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Q: Give a detailed numerical example of the Aitken approximation method.

A: I have provided the solution with one example

Q: Find the smallest positive root by using fixed- point method f (x) = In(3x)– x² +2 %3D with three…

A: Given: fx=ln3x-x2+2. We have to find the smallest positive root by using fixed-point method with…

Q: How is the Chain Rule applied when finding dydx implicitly?

A: According to the question, we have to explain the chain rule when used in the implict function.…

Q: Find the orthogonal trajectories of x² + y² – 2cy = 0

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Q: Find the critical numbers of the function.…

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Q: Find the linearization of f(x)=ln(x2-3) at suitably chosen integer near X=2.1. Then use the…

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Q: (1) 1-tank x=sech'x

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: 3. One of the methods used to eliminate arbitrary constant is by isolation of arbitrary constant and…

A: Here, to write the other method to find the arbitrary constant of the differential equation.

Q: у" - In x

A: Given: y''=lnx

Q: 8. Find the Laplacian of Ø = xy²z³

A:

Q: Find the positive critical point of the function f(x) 2+3

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Q: tion k passes through the points (4.

A: Please refer to the image below

Q: How can I find the gini index of y = x^1.1?

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Q: Find the smallest positive root by using fixed-point method f(x) = In(3x)– x² +2 with three…

A: we have f(x)=ln(3x)-x2+2=0 x2=ln(3x)+2x=ln(3x)+2using fixed point iterationxn+1=ln(3xn)+2take…

Q: Numerically integrate f (x) = x³ + 3x? + 4x = 2 using Single-Trapezoidal Rule. 6 from a = 1 and b -…

A: (1) solution

Q: 3. x - y=t + 3 4. x = VT-T; y =t- 3t 5. x = vE + 2; y = t² - 3

A:

Q: f(x) = lim (6x + 2 4x + 3) = 6x + 3 Ax-->0 f (x) = lim (6x + 2 4x + 2) = 6x + 2 %3D 4r-->0 f (x) =…

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Q: Find the general solution using Methods of Undetermined Coefficient and Variation of Parameters.…

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Q: Explain theorem of Wronskians of Solutions?

A: To Find : Define the Theorem of Wronskians of solution

Q: Find the maximum and minimum value of f (x,y) =x' + 3xy² – 3x² – 3y² +4 = X" - -

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Q: 6 Find the critical numbers of the function f(x) = x5 - * – 12x2 .

A: The given function is  fx=x65-12x12.

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: Finds the solution (roots) f (x)=x^3+ x-1=0 using fixed point iteration process

A: The given equation is. fx=x3+x-1=0                                                ...........1 Here,…

Q: What values of a and b make ƒ(x) = x3 + ax2 + bx have a local minimum at x = 4 and a point of…

A: Given: fx=x3+ax2+bx fx has a local minimum at x=4 . fx has a point inflection at x=1 . Since fx…

Q: 2. Integrate the function (x+2/x)ax using multiple-application trapezoidal rule with n= 3

A: Trapezoidal Rule: ∫abf(x) dx≈∆x2(f(x0)+2f(x1)+ ... +2f(xn-1)+2f(xn))where ∆x=b-an

Q: Explain how successive over relation is obtained from the Gauss-Seidel method.

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Q: The value of Wronskian of two functions y, =7* and y2 =7** is

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Q: Find the critical numbers of the function f(x) = x – 12x2.

A: This is a problem related to derivative of the function. Based on the general formula we will…

Q: So x, = c,e +c,e", and x, = 3c,e" +c,e" Sketch the trajectories in phase plane 2 -2 -2 Comment

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Q: find orthogonal trajectories of   x2+(y-c)2=c2.

A: x2+(y-c)2=c2 now differentiating both side with respect x , we get 2x+2(y-c)dydx=0 or, dydx= -x(y-c)…

Q: Find the linearization of ƒ(x) = 2x at x = 0. Then round its coefficients to two decimal places.

A: Given function is,

Q: 12. Differentiate the function (use chain rule): y = 2x2 Vx+1'

A: To differentiate the given function

Q: I Sdve for dydx using the four-step rule 2. Y = x- x 2.

A: