1. Find the root of: f(x) = e^x - 4x^2. Newton Raphson Method %3! Initial estimate : 1 Stopping Criterion : f(x) = xxxxx X 10^-10

Q: By using the definition of hyperbolic functions as exponential functions, show that sinh 3x = 3 sinh…

A: handwriting solution

Q: give 3 examples of the reciprocal rule of integration formula

A: The reciprocal rule for the integration is: ∫f'(x)f(x)dx=ln |f(x)|+C

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

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Q: Show that √(10x + 1) and √(x + 1) grow at the same rate asx→ ∞ by showing that they both grow at the…

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Q: Suppose that 2J of work are needed to stretch a spring from its natural length to a length 1m beyond…

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Q: Find the roots using secant method. Stop until at 15th iteration or when approximate percent…

A: clc;clear all;close allx=-1:0.01:2;y=exp(x)+x-4;plot(x,y,'color','blue')xlabel('x')ylabel('f(x)')ax…

Q: Find the root of fx)=ln(x)-cos(x) by Newton Raphson method take xo-0.5 Bisection method (1, 2)…

A: "Since you have posted a question with multiple subparts, we will solve the first three subparts for…

Q: Verify Eq. (2): cosh2 x - sinh2 x = l.

A: To verify Eq. (2): cosh2 x - sinh2 x = l.

Q: Q-3-Edaluate the fallowing Integration 1- X3 x21 2. 2- X+1

A: Use the partial fraction to solve the given problem.

Q: 3. Solve for the root with starting at x=1 and Ax=+0.1 and tolerance in function error of 0.001 Зx2…

A: (3) Given that f(x)=3x2+ln2x-6,  x0=1 Using the newton raphson, xn+1=xn-f(xn)f'(xn) At n=0,…

Q: Determine the positive real root of ln(x^2)=0.7 using three iterations of bisection and…

A: The bisection method uses the midpoint of an interval to perform the iterations to approximate the…

Q: 3. f Arccos 2xdx

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Q: 2 cosh(2x) – sinh(2x) = 2

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

A: Following formulae are used to solve first question

Q: data point at x1= 1, x2=4, x3=6 and x4=5 were used to estimate ln 2 with a third-order newtons…

A: To obtain the required polynomial equation, use the following Newton's divided difference…

Q: Log Activity CALL l.y=log4 (3x2 -5x) In 9x4 2.y= 3.y= Inx3 X-5

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Q: Find the fourth iteration value in finding an extremum (maximum/minimum) value of f(x) = 5sin2x -…

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Q: how do we identify the minimum and maximum value of the graph of a function at a given intetval?

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Q: Verify Eq. (2): cosh 2 x - sinh2 x = l.

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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: dervivative of (ln(cosh(x)))3

A: Given data:     The given function is: y=(ln(cosh(x)))3. STEP-1 Assume u=coshx and differentiate it…

Q: 4. Find at the point (1,1,1) if ln(xyz) = 1 əx

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Q: Find the root of the equation fx=ln(x)-5+x in the interval [3.0, 4.0] using Regula Falsi method. Use…

A: Formula: Formula to obtain the iterations in Regula Falsi method is, xn+1=x0-f(x0)x1-x0f(x1)-f(x0).…

Q: A metal storage tank with fixed volume V0 = 360π m^3 is to be constructed in the shape of a right…

A: To find: The dimensions will require the least amount of metal. Given information: A metal storage…

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

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Q: Find ∫cosh 2x sinh2 2x dx.

A: To find the value of the integral∫cosh2xsinh22xdx

Q: 3 11 lim *+3 9. x→2 2х - 4

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Q: Solve using Euler’s Method. Approximate up to 5 decimal places.

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Q: rIn 2 cosh x dx. Vsinh a x + 4 sinh x +2

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Q: 8. The value of f sinh* x cosh³ x dx

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

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Q: 1. f(X)= xpi - pi(x) + pi/x + pix - cos (pi)

A: Given, fx=xπ-πx+πx+πx-cosπ We know that dxndx=nxn-1daxdx=axlnx

Q: Use Newton's method to find a root of x* – 5x³ + 9x + 3 = 0 accurate to 6 decimal places. Perform…

A: Newton method is generally known as Newton Raphson method. It is a iterative method to find the…

Q: Find the possible values of cosh x that satisfies sinh²x – 3 cosh x + 3 = 0

A: We use the following identity to solve question 1). cosh2x - sinh2x = 1

Q: The critical speeds of oscillation, à, of a loaded beam are given by the equation: 23 – 3.25022 + 1…

A: W have to use Newton's method to solve the value of lambda.

Q: Solve.  ln(sqaure root of z/xy)

A: We are given logarithm expression as

Q: Find the fourth iteration value in finding an extremum (maximum/minimum) value of              f(x)…

A: The Newton Raphson method is used to solve an equation numerically. When the extremum of a function…

Q: The approximation of the root x* of the function f(x) = -x + sinx-1 accurate to within 10-3 using…

A: Needs 2 iterations

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

A: We have given

Q: 1- Y= sin( coshx log2 2 ) 2-Y= sinx.coshx. log2 2 3 - y = In Vx. sin x

A: Apologize  that we are permit to do first question of the multiple questions but still I am doing it…

Q: Find the orthogonal trajectories of family of curves y = ax5 (SOLVE BY USING DIFFERENTIAL…

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Q: Use linear approximation or differentials to estimate v80. Show your work.

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Q: data point at x1= 1, x2=4, x3=6 and x4=5 were used to estimate ln 2 with a third-order newtons…

A: As we can see given points are not equidistant so for finding ln 2 we will use Newton's divided…

Q: if 2 tanh x.In x = sinh' (sin x)+logcos dx dy Q5/ Find

A: To differentiate the given function.

Q: Compute for a real root of 1 2 cos Vx – sin vx = accurate to 4 | 4 significant figures using…

A: 2cos(33)-sinx=14;   x0=π f(x)=2cos(33)-sinx-14 f(x)=0 ⇒2cos(33)-sinx-14=0 x=cos-11214+sinx3=ϕ(x);…

Q: 2. Compute for a real root of 2 cos x - sin /x = 4 accurate to 4 significant figures using…

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Q: When should I use partial integration and when should I use substitution?

A: When should I use partial integration and when should I use substitution.

Q: 1 lim, „(e* + x)÷ +00

A: Explained below

Q: In( cosh(3x) - sinh(3x) )=

A: