x+1 Q1/ Prove that coth-1x = x-

Q: Use Newton's method with initial guess x1 = 1 to compute two successive approximations of the…

A:

Q: 4) Find linear ditterental equation with costnt y-ac'+cadk Lomageneas coetfients whose general…

A:

Q: (5) Evaluate the definite intergral [/³ (sec²x+3x)dx. /3

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Q: of f(x, y, tion of ve

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Q: (- 0,a) is measurable.

A: Note that, every interval is measurable.

Q: 1. The first approximation of the root of xlogx - 1.2 = 0 in [2,3], by Regula Falsi method (False…

A:

Q: 2 - ) at x = 4 1+ x)

A:

Q: Find the absolute max and min of the function F(x)= 2sin(x)-cos2(x) on the interval [-π, π]

A:

Q: 1. Determine one real root of the equatione O using Fixed Point Iteration with ao O until %ER < 20%

A: Given equation is   e-x-x=0 with x0=0 Also, given that ER≤20% Rewrite the equation  e-x-x=0⇒x=e-x In…

Q: Prove: cosh 3x = 4cosh'x- 3 cosh x %3D

A: We will solve the following.

Q: id I prove this qa is not to zero correctly? Please look over my proof and qa is not equa

A: Proof by contradiction:  Argument by contradiction is a type of proof in logic and mathematics that…

Q: The interval on which f(x) = 5 – 12x2 – 4x³ is concave up is: (-∞, –1) © (-1, 00) O (-0, 1) • (1,00)

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Q: 2) Use Newton's method to approximate the zero in f(x) = - x3 + 3x-x + 1, or explain why Newton's…

A: Consider the given function,

Q: Q1- Prove that coth x = 2 csch 2x + tanh x

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Q: Q1- Prove that coth x = 2 csch 2x + tanh x %3D

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Q: 2) Find FCO), if it exits Punctien f(z) - 2 if x raticnal if x irraticnal

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Q: Use Fixed-Point Iteration Method to obtain a real root of x^3-5x+1=0 with x₀=0 until absolute error

A: Solutions

Q: Find the approximate root in 5th iterations of the function f (2) = x3 - 2a - 5, xo 2.5 by x = 2x +5…

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Q: What are the critical points of sin(x2-1), at the closed interval [-1,1]?

A: Given: The critical point is a funtion is the point where the derivative of the funtion is zero.…

Q: Prove that sinh−1(x) = In( x+Vx2 +1)

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Q: 3) Use the Intermediate Value Theorur to show that there ís a root of the equation Make sure you…

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Q: ) Use Taylor's formula to estimate the error in the approximation In(x) ~ P3(x) or all x in the…

A: Since you have posted multiple questions but according to guidelines we will solve the first…

Q: . Determine the upper bound on the error in the approximation: x2sinx3 x. - if x|<0.8 6.

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Q: Use Newton's Method with the function f(x) = x² – 2 and initial value xo = 1 to calculatex1,X2, X3 .…

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Q: 4. Determine the root of F(x) = 7 sin(x)e--1 using secant method with 3 iterations given X- = 0.5…

A: f(x) = 7sin(x)e-x - 1The iteration for Secant method is given as: xi+1 = xi - f(xi)(xi-1 -…

Q: Show that x + is increasing on [1, 0).

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Q: Use Newton's method to obtain a root for x^3 - 2x + 5 = 0

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Q: 29- For uhat values of a and b is ax+2b x+3a-b くXS2 3X-5 Continuous at every X

A: Dear,as per company guidelines we can answer only one question at a time, kindly post other question…

Q: Use the Intermediate Value Theorem to show that 2x – 3 - if – 3 0 has a zero on the interval [-2,…

A: First compute the function if they are continuous then apply the intermediate value theorem.

Q: What is the second iterative value of the root f(x) = x2 - 3. with the initial bracket [1, 2] using…

A: To find The second iterative value of the root of f(x) using the bisection method.

Q: See image below.

A: We subtract x from both sides

Q: The first derivative of the power series 3x2 3x f(x) = 3 1! 3x3 3x4 325 %3D - 2! 3! 4! 5! • is

A: Formulae: 1. e-x = 1-x/1! +x2/2! - x3/3! +x4/4!- ....... 2. d/dx{ e-x} = - e-x   Answer: f'(x)= f(x)

Q: Use the Successive Approximation Method, to find correct to tigures a real root oF the fun čtion…

A: The given equation,extanx-1=0

Q: Verify mean value theorem for ƒ(x)=x' – 5x+6 over the interval [1,3].

A: Please refer to the image below

Q: 13,4) f(x.y) =In(x + x² +y² If Find x

A: f(x,y) = ln (x+x2+y2)∂f∂x=∂ ln (x+x2+y2)∂x=1 (x+x2+y2)×(1+12x2+y2)×2x

Q: Find all critical numbers of f(x)=3x+sin(3x)

A: Given,   f(x)=3x+sin(3x) We have to find all the critical numbers.

Q: (- 0 ,a) is measurable .

A: Given a statement

Q: of f(x) =x – 3 by False position method with the interval [1,2], for Q1) Find the root three…

A: The given function is  f(x) = x2 - 3 To find the root using false position.

Q: Fix a constant r>1 Using the Mean Value Theorem that enx > 1 + x for any fixed x >0 prove

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Q: Prove LHS is equal to RHS: 8-(4x-5)=x-7

A: Given:

Q: hraj h(x) = 3x-2 x347

A:

Q: 29 - For uhat values of a and b is ax+2b x+3a- b くXS2 3X-5 Continuous at every X ?

A:

Q: Find the positive root of the equation x + 2x2 + 10x - 20 in the interval [1,2] using Regula Falsi…

A: Let, the given function be: f(x)=x3+2x2+10x-20 And, the formula of the method is:…

Q: If g(x) : 8 + cosh(9x) find g'(x) 8+ cosh(0)

A: Answer and explanation is given below

Q: by thể differen ntial equation on associated with this sy

A: In this question, the concept of Laplace Transform is applied. Laplace Transform The Laplace…

Q: Use Newton Raphson Method to obtain a real root of x^3-5x+1=0 with x₀=0 until absolute error

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Q: Show that cothx x+1 In X-1,

A: Solution

Q: Use Newton's method with initial guess x0 = 1 to compute two successful approximations of x3-2= 0.

A: Please see the answer below

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.