Find a quadratic polynomial such that f(1) = 5, f'(1) = 4, and f"(1) = 8.

Q: Find the general solution using Reduction of Order: y''=2lnx

A: Explanation of the answer is as follows

Q: Compute for a real root of sin Vx – x = 0 using three iterations of Fixed-Point Iteration Method…

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Q: Question 1 Find the total differential of the function z = 7x³y8 Odz = 7x¹y³dx + 7x³y+dy dz =…

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Q: Find the local linear approximation of f(x) at 4 + x xo = 3, where Ax = x – 3. NOTE: Enter the exact…

A: f(x)=14+x

Q: Estimate the root very near x = 0.2 of 2(x*)* - 3(x*} + 1 = 0 using the Newton- Raphson Method with…

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Q: Find a root of an equation f(x)=x3-x-1 using Newton Raphson method.

A: We will find out the required root.

Q: f(x) Vx+1

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Q: Find the exact error in approximating ln(sec(−0.4))by its fourth degree Taylor polynomial at ?=0.

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Q: 2- Find the approximate roots of the following equation f(x)= 4x – x² -2 = 0 on [0,1], by using…

A: According to the given information it is required to find the approximated roots of the equation…

Q: F(x)= ]7+1 3x t dt 2 F'(x) = %3D

A: We will find the derivative using Fundamental Theorem of Calculus.

Q: Use Milne's method to obtain the value of y(0-3).

A:

Q: Use the derivative to find the critical point of f(x) = Ax² + Bx + C. Assume that A, B, and C are…

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Q: Find the differential operator which will annihilate the function 2x + r³ – sin 2r.

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Q: 2 that also passes Write the equation for a quadratic function f(x) with roots at x = 7 and x =…

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Q: The length and width of a rectangle are measured as 35 cm and 28 cm, respectively, with an error in…

A: To determine the maximum error in the area.

Q: xdx S- can be solved by either algebraic subsitution or integrataion by parts. Vx-1

A: We have to find the following integral

Q: Use differentials to approximate V36.1. 3.

A: Consider y = root x.Let take x = 36 and delta x = 0.1.Find delta y as follows.

Q: 5

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Q: Find a double root of the equation f (x) = x' -x -x+1 = 0 by generalized New- ton's method.

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Q: Use a linear approximation (or differentials) to estimate the given number. (1.999)3

A: First I have find the linearization of x^3 near x=2 and then find the required approximated value.…

Q: 2. Compute for a real root of Sin Vx – x = 0 using three iterations of Fixed-Point Iteration -…

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Q: Find the derivative of the function. h(x) = In[(2x + 8)(3x +6)] a. (2x + 8) (3x +6) 1 1 Ob. (2x + 8)…

A: The objective is to find the derivative of the function h(x) .

Q: Use differentials to approximate the value of <2.1.

A: Given  Find the value of 52.1

Q: Find the approximate root in 5th iterations of the function f (x) = x- 2x-5, xo 2.5 by x = V2x +5…

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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: Compute for a real root of sin Va – x = 0 using three iterations of Fixed-Point Iteration Method…

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Q: What kinds of changes occur in the Coefficients of a Nonbasic Variable when the original model is…

A: Answer is explained below

Q: 5) Form a DE by eliminating the arbitrary constants from the equation y = asin(4x + 1).

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Q: Find the derivative using the long method 3 u = t2

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Q: Find a root of an equation f(x) = 0.842x²-x+ 0.2 using Newton Raphson method

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Q: Determine the degree of the Maclaurin polynomial required for the error in the approximation of…

A: Consider the given: The Maclaurin series for sin x centered at x = 0 is:…

Q: Find the differential of the function.

A: Differentials are infinitely small quantities. We usually write differentials dx, dy, dt (and so…

Q: Find the derivative. |4t +5 dt O A. V4x+5 O B. V4x+5 - 5 2 OC. V4x +5 OD. (ax + 5)/2

A: It is given that, y=∫0x4t+5 dtWe have to find the derivative.

Q: Consider the function f(x) = x³ + 2x + 5. Estimate the root to eight significant digits using Newton…

A: The general form of an equation of degree 3 is given by ax3+bx2+cx+d=0, where a≠0. In this problem,…

Q: Suppose that a car accelerates at a rate of a(t) = t – 7 meters per second. Use the Fundamental…

A: ANSWER :

Q: Find one of the roots of the function using Regula-Falsi method. £ (x) = x- V+1

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Q: Find the quadratic approximation to ƒ(x) = 1/(1 - x) atx = 0.

A: Given,  f(x) = 1/(1 - x) at x = 0

Q: In(4z+10) Find the derivative of the function f(z) = z'sin(9z + 12) + %3|

A: Given:- f(x)=x4sin(9x+12)+ln4x+10x3 To find:- Derivative of given function

Q: Find the serial solution of the differential

A: We have to find out the series solution of the differential equation y''-xy=0 at the neighborhood at…

Q: Find y double prime by implicit differentiation8x^2+y^2=4

A: We have given

Q: Find the approximate root of y = 2x2 + 4x – 6 when x = 0.01 using differentials. -

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Q: Find a root of an equation f(x) = x^4-2 using Halley's method.

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Q: Find the root using newton raphson method for f(x) = sin(x) − x²

A: Given function is f(x)=sin(x)-x2 From the given equation, it is clear that 0 is one of the root of…

Q: Compute the derivative of x(x + 2) (2x + 1)(3x + 2) y = (a) directly using the Chain and Product…

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Q: Find the general solution to the DE using the method of Variation of Parameters: у" — Зу" + Зу' — у…

A: The solution is given as

Q: Find a differential operator that annihilates the given function. xe3xsin5x

A: given function is                                                      f(x)=xe3xsin5x we have to…

Q: A body is projected vertically upward such that is height from the ground in feet is h = 50t –…

A: Given, height from the ground in feet is h = 50t – 16.1t2 where t = time in flight in seconds The…

Q: The length and width of a rectangle are measured as 38 cm and 34 cm, respectively, with an error in…

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Q: find all solution of z   sinh(2z)=-1

A: Consider the provided equation, sinh2z=-1 Find all solution of z. Apply the trigonometric…