III. Solve the hyperbolic function of the following. 1. Find x in coshx = sinhx + 2sechx. 2. Express sinh*x in terms of hyperbolic cosines and multiples of x, and hence solve 2cosh4x – 8cosh2x + 5 = 0. 3.Prove that coshx – coshy = 2sinh (**) sinh ().

Q: determine the annihilator of the givenfunction. F(x) = sin2 x cos2 x cos2 2x.

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Q: Consider the following IVP: x" + 4x = t+4 ; x(0) = 1, x'(0) = 0 Find the general solution. A x (t)…

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Q: V3 B) If sinh 0 Find cosh 0, tanh 0, coth 0. %3D 2

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Q: 6. Find all the values of z satisfying sinh z = = -j1.

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Q: 8F OF OF 1. Use the formulas above to find and ду ax exy + sin (xyz) + In (yz) = 4 – z

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Q: 2- Find the positive root of f(x) =xe - cos (x) with an error tolerance -0.005% by using a) The…

A: (Solving the first three subparts as per our guidelines) Solution: The function is fx=xex-cosx Error…

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Q: 57 6. Find an equation of the tangent line to y = f(x) = cos²(x) at %3D

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Q: 1. Calculate for one real root of tan r 4x with ro 1.2 up to four decimal places using the…

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Q: 17. Consider the DE y"+by'+cy = 0. If y₁ is a solution of the equation, what conditions must be…

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Q: determine the annihilator of the givenfunction. F(x) = sin x cos3 x.

A: We have to determine the annihilator of the function: Fx=sinxcos3x Annihilator is the set of linear…

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Q: 1. Use fixed-point method to locate the root of f(x) = sin(vx) – x Use an initial guess of xo = 0.5…

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Q: Use the Newton-Raphson Method to approximate the root of f(x) = 2 cos(x) – 2x + 1.

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Q: 8 (a) To evaluate the integral J cos xdx by using the reduction formula of Cosine function.

A: We have to use cosine reduction formula.

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Q: y" + 3y' + 2y = e* (t2 + 1) sin(2x) + 3e- cos x + 4e"

A: Answer

Q: 6. S(x)= In(tanh 5"

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Q: 1. Solve the hyperbolic function of the following. i. cosh (-2 + j3) in the form of a + jb ii. sinh…

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Q: 1. Calculate for one real root of tan x = 4x with xo 1.2 %3D up to six decimal places using the…

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Q: 1. Use Newton-Raphson method to find sixth iteration of a real root of the equation: cosx-xe* =0…

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Q: 1) f(x) = In 2x + sin x - 2e* , in the interval [0.4, 0.6]

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Q: Consider the following IVP: " + 4x = t+4; x(0) = 1, x'(0) = 0 Find the general solution. (A x(t)…

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Q: 1. Solve the hyperbolic function of the following. i Prove that coshx – coshy = 2sinh (*) sinh ().…

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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.