Use newton's method to find an approximate solution of ln(x) =3-x. Start with x0 = 10 and find x2.

Q: use the variation-of-parameters method to solve the given differential equation. Q. y′′+y =tanx.

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Q: If the rate of change in the microwave rays M(x), where x is the distance, decreases with a rate…

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Q: Use Newton’s method to find an approximate solution of 3 - x = ln x. Start with x0 = 2 and find x2.

A: Given: 3 - x = ln x That is  f(x)=3 - x - ln x Initial value x0 = 2.

Q: By using the differential operator D and it's inverse, solve this equation: y"+y=sin(x)

A: Follow the procedure given below.

Q: Differentiate y = /sin(x² + 3)cosx

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Q: Solve the differential equation: y = 3x +log P.

A: Given equation is y=3x+log P Let us consider P as a constant and then dydx=ddx(3x + log…

Q: solve the differential equation

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Q: Find the general solution using reduction of order. 1. y''=ln(x)

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Q: Find the indicated derivative and simplify. [6x log x°] dx [6x log x ]= 125 dx (Type an exact…

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Q: A population of insects grows at a rate that is given by dN = 0.078N dt - If there are initially 100…

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Q: (x² ln x dx

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Q: 2. Find a real root of 3x – logi0 x – 8 using the Successive Approximation method. Correct to four…

A: As per the company's guidelines, we are supposed to solve first question for you, kindly repost…

Q: Solve the differential equati on. dz (log x) = –(log z) dx X

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Q: For y=ln2x, determine the equation of a tangent line parallel to 2x-3y+1=0

A: here we find the equation of a tangent which is parallel to 2x-3y+1=0. y=mx+c slope = m.

Q: find a real root of the equation xe^x-2=0 using Newton's method

A: Explanation of the solution is given below...

Q: Solve by hand function bellow using Newton method. Repeat 5 times. (5 iterations) f(x)=x® +4x2-10

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Q: Use Newton’s method to estimate the solution of the equation x2 +x−1 = 0. Start with x0 = 1 as…

A: Let, f(x)=x2 +x−1  Then find f'(x) using power rule.

Q: Let 2.13x = 1, the Newton's Method to find the value of x with correct to 7 decimal places

A: The given equation is;  2.13x=1.

Q: Find dy/dx by implicit differentiation. 5 5 y3 dy/dx = (Express your answer using positive exponents…

A: We have given 5/x^3 + 5/y^3 = 1

Q: )=1/x. Using this, compute the

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Q: Find a root of an equation f(x) = cos(x) - − using Newton Raphson method

A: Let us start solving the problem step by step  Given  Cos(x)-(x/6)=0 Let f(x)= cos(x)-(x/6) We will…

Q: Find the absolute maximum value of ƒ(x) = x2 ln (1/x) and say where it occurs.

A: We need to find the absolute maximum value of the function

Q: ln (x−4) + ln (x+1) = ln (x −8

A: We can use properties of log to slove the given problem. If we have  ln x + ln y Then we can write…

Q: Solve the differential equation for y if (1+9x²) dx %3D

A: Here we have to solve the differential equations,  1+9x2dydx=1.................................(1)

Q: Find the given derivative 6 Dx 7x 1 Dx 7x 5 LN +

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Q: Prove that E = ehd.

A: By the defination, fx=fx+h....1∆fx=fx+h-fx∆fx=Efx-fx∆fx=E-1fx Therefore, ∆=E-1E=1+∆.....2

Q: Find the slope of the tangent line to the exponential function at the point  (0, 1). y = ex/3

A: Slope of tangent line is derivative of the given function at that point.

Q: use the Newton's Method to solve the equation x+lnx=2

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Q: Solve ∫xn ln x dx in tegration by Parts?

A: Given:               ∫xn ln x dx Apply integration By Parts:              ∫xn ln x dx=ln x∫xn…

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

A: Given  Find the value of 52.1

Q: Investigate the root of the equation x+Ln x-5 = 0 in the range [3.2,4] using the Regula-Falsi…

A: Consider the given equation whose root is required to calculate.

Q: The intensity L(x) of light x feet beneath the surface of the ocean satisfies the differential…

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Q: Find the x-value where the maximum value of y=sinx−7x^2 occurs. When you need to solve for an…

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Q: = (+ Use the fact that i and -i = to solve the differential equation dx4 + y = 0.

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Q: The equation x ln x = 1 has a single solution, Give a short justification for this the claim.

A: Consider the given equation xlnx=1

Q: Use the Newton-Raphson method to find the root of sin(x) = e=x For this problem, use initial guess…

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Q: 19.) [(ycoth y² )log°(sinh y² )dy

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Q: Approximate the positive root of the equation x -sinx-1=0 , by performing five iterations of the…

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Q: How is ln x affected if x is multiplied by et?

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Q: When sugar is dissolved in water, the amount A that re- mains undissolved after t minutes satisfies…

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Q: Solve the differential equation. (Use C for any needed constant.) 7 + Vr 7 + Vu du dr

A: Given differential equation,

Q: If the rate of change in the number of cows, W, in a population is proportional to 150 - W(t), where…

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Q: V34

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Q: x" + 2x' + x = e° -t.

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Q: The intensity L(x) of light x feet beneath the surface of the ocean satisfies the differential…

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Q: Find the root of x² - 1000 = 0 using Newton's law of approximation

A: We have to approximate the root of x7-1000=0 now we have f(x)=x7-1000,  f'(x)=7x6 Newton's law of…

Q: x dy -ydx -Vx²_yz dx =0

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Q: Instead of approximatingln x near x = 1, we approximate ln (1 + x) near x = 0.We get a simpler…

A: Given function is fx=ln1+x. ∆x=0.1,f'a=1

Q: Solve for the second derivative(y") of the following and simplify the final results. Show complete…

A: Given. ⇒4lntan-1x=1-y⇒y=1-4lntan-1x Taking derivative with respect to x, we get…

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.