12. Given the following function 2 x +0 f(x) = x2 a. Given 0 < f'(x), determine its condition. b. For equation x2 = 2* , calculate all its rational solutions. (hint: use contradiction) For equation x2 = 2*, prove that it has three distinct solutions (must be real numbers). (hint: drawing graphs could help finding the solutions) с.

Q: 5) Find the general solution by using reduction of order method to (x² + 1)y" – 2xy' + 2y = 0 given…

A:

Q: 1) a) Derive the secant method to solve for the roots of f(x)=0 nonlinear equation, b) Use the…

A: Detailed explanation mentioned below

Q: Find f(x) by solving the initial-value problem. f '(x) = 6ex − 10x; f(0) = 15

A:

Q: Find a particular solution y, of the following equation using the Method of Undetermined…

A: The solution is given as

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A: Comparing it with Auxx+Butx+Cutt form, we get A=20, B=-1, C=-1. Then, B2-4AC=(-1)2-4(20)(-1)=1+80=81…

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A:

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A: To Determine: find the x-value of the point on the curve that is closed to the point (8,0) Given: we…

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Q: Consider the following initial-value problem. f'(x) = 6x2 - 4x, F(1) = 3 Integrate the function…

A: *concept:- integration to be perform.

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A: Given integral is  ∫tanh52xsech2xdx

Q: Consider the following initial value problem. y+ 5y + 6y = 0, y(0) = 3, y'(0) = 6, where 3 > 0…

A: NOTE: Refresh your page if you can't see any equations. . find roots for the homogeneous system

Q: 14 (1). If f (x, y) = -x³ + y* - 3xy + 9x? + y, then in the process of obtaining its critical points…

A: Given that fx,y=−x3+y4−3xy+9x2+y

Q: Consider the following initial-value problem. f'(x) = 6x2 – 8x, f(3) = 21 Integrate the function…

A: Given: f'x=6x2-8x, f3=21   As we know the Power rule: ∫xndx=xn+1n+1+C

Q: "(2) – 16f(2)) sinh(4x) dr Find the value of in terms of f(0) if f(a) = f'(a) = 0. %3D f(0) O f(0)…

A: See the calculation below  Fourth option is correct

Q: 9x²- e2x 2 Given by a function of x is equal to v1 – cos²x + = 0. find the roots of equation with…

A: We can solve this by bisection method

Q: Find the absolute maximum value of f(a) = x2- 2x +9 over the interval [0,5] The value C for the…

A: Use derivative and integration for the following question.

Q: ind the solution to the eguation 2x² – In-- 5x = 0. Use a tolerance of function error of 0.001| 3x…

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Q: Suppose that we need to find the solution of y" = y², y(a) = 0, y(b) = 2 by finite difference…

A: This question is about application of numbers theory

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A:

Q: If ä – i – 6x = 0 with x(0) = 1 and (0) = a, determine the value(s) of a such that the solution…

A: Given,        x¨-x˙-6x=0   with  x(0)=1    and    x˙(0)=a

Q: Find a particular solution y, of the following equation using the Method of Undetermined…

A: We have to solve given problem:

Q: Find f(x) by solving the initial-value problem. f '(x) = 8ex − 4x; f(0) = 12

A:

Q: i) Given that f(x)=3cos5x+sin5x. (a) Express f(x) in the form Rcos(5x-a) where R>0 and 0° < a <90°.…

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Q: Find a particular solution y, of the following equation using the Method of Undetermined…

A: Given differential eqution y''-y'-2y=3x+3

Q: Find a particular solution y, of the following equation using the Method of Undetermined…

A: We have to find Perticular Solution for given differential equation by method of undetermined…

Q: Find a particular solution y, of the following equation using the Method of Undetermined…

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Q: 1 Considered the area of a trapezoid is 50 sqm and the height is described by a number. Bases are…

A: Area of a Trapezoid = 50 We know that area of a trapezoid = 1/2 h(b1+b2) Let the height be x Bases…

Q: 1. Given f(x,y) =1+0.25y-e* with y(0)=- in the interval [0, 1]. Solve the IVP by using 3 Euler's…

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Q: The function f(x) = X = (6x 3) e5 has one critical number. Find it.

A: Given function ,   f(x)=(6x-3)e5x

Q: Consider the following initial-value problem. f '(x) = 9x2 − 8x, f(3) = 47 Integrate the function  f…

A: NOTE: Refresh your page if you can't see any equations. . take integration  .............(1)

Q: Use the method of variation of parameters to solve the initial value problem x' = Ax + f(t), x(a)=…

A: We have to find the solution x(t) using the method of variation of parameters.

Q: 12. Find the general solution using Reduction of Order: a) y"= 2ln x b) y" + y' = cos 3x

A: We have to find the general solution: y''=2lnx. Here, the value of y1 is not given.

Q: 1. Determine the positive root of f (x) = x³ + 2x – 2 = 0 using the Newton- Raphson method and an…

A: Here f(x) = x3 + 2x - 2 ∴ f′(x) = 3x2 + 2x0 = 0

Q: 14 (1). If f (x, y) =-x' + y* - 3xy + 9x? + y, then in the process of obtaining its critical points…

A: The given function is fx,y=-x3+y4-3xy+9x2+y partial derivatives are fx and fywith respect to x and y…

Q: Q2 A rod of length 2 m is fully insulated along its sides. The temperature at x is initially TX 100…

A:

Q: Suppose f(x) is positive, continuous, and f'(x) < 0 for all æ in [ – 8, 4], and| f(x)dx = 76 and L…

A: Concept: Mean value theorem: The mean value theorem states that if a function f is continuous over…

Q: Q3. Use the finite-difference approach with the one iteration of Gauss-Seidel method to solve the…

A: Given that d2Tdx2+0.0120-T=0 and T0=40, T10=200. By using the numerical values,…

Q: Find a particular solution y, of the following equation using the Method of Undetermined…

A: Given differential equation is  y" + 15y = 3e^8x

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A: Since we only answer one(first) of the multiple question from the given multiple no. of question.…

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Q: 5- For each of the following equations, determine an interval [a, b] on which fixed-point iteration…

A: We are entitled to solve one question at a time. As all parts are different, so we are doing first…

Q: Use the method of variation of parameters to solve the initial value problem x' = Ax + f(t), x(a) =…

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Q: Does the function y(t) = 2e -5t satisfy the following initial value problem? y'(t) – 5y(t) = 0, y(0)…

A: Given function yt=2e-5t. Given initial value problem y't-5yt=0, y0=2. The main objective is to tell…

Q: b. Obtain the solution x(t). æ(t) = h(t-5) sin(47(1- 5))- c. Express the solution as a…

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Q: For what reasons do we implement and Df(xk)wk = − f(xk) (*) Xk+1 = xk + Wk in a step of the…

A: As per the equation given option C and ''a'' are true .

Q: Find a particular solution Ур of the following equation using the Method of Undetermined…

A:

Q: 5) Find the general solution by using reduction of order method to (x2 + 1)y" – 2xy' + 2y = 0 given…

A: Use the procedure of reduction of order to solve the given differential equation as in next step.

Q: Use the method of variation of parameters to solve the initial value problem x' = Ax + f(t), x(a) =…

A:

Q: f' (x) = +3.f(1)= %2 %3D

A:

Q: The function f(x) = (6x+5)e^4x has one critical number. X= ?

A: Proceed as shown below...