1 Find the interval and radius of conv. of- '(1–4x²)

Q: (5) Find the particular solution passing through the point (1,8) How does this solution behave as t…

A: Sol

Q: A number of the form iy is called pure imaginary

A: A number of the form z = x + iy is known as complex number, where x is real part and y is imaginary…

Q: List all points on the elliptic curve defined over F13 by Y2 = X³ + X + 12,

A: Given the elliptic curve defined over F13 by Y2=X3+X+12.

Q: On (-∞, ∞), three functions y₁(x) = cos 2x, y2(x) = sin² x, y3(x) = cos²x are linearly independent…

A:

Q: Find the orthogonal trajectories of the family of curv

A: In this question we will use basic of calculus i.e concept of orthogonal trajectory. We will simply…

Q: The integration expression Jsin(3In(x)+ 4)cos(3In(x) + 4)dx must be transformed into using suitable…

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Q: Find the of Integ ration f(u)= tanu + Cos 2u. %3D

A: Given information is :

Q: The normal line to the curve y = -2x2 at a point in the fourth quadrant passes through the point…

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

A:

Q: Prove 9 coshx – 5 sinhx = 15

A: This is hyperbolic function equation so we want to find x value by thi equation so. firstly, we…

Q: tion of all components of v(3) correct to two decimal places.

A:

Q: 2. Write closed Newton-Cotes formula with error for n=1, 2, 3 and then solve integral S* sin(x) dx…

A: The Newton cotes formulas are closed when the endpoint of the closed interval is used as a node. The…

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

A: We will solve the following.

Q: The 2nd derivative of the given functions is 3 ponts y = 3 cos (4x- 5) None of the above -48 cos…

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Q: 1.Find the interval and radius of conv. of ln(1 – x²) ?

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Q: Verify the statement by showing that the derivative of the right side equals the integrand on the…

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Q: Solve 2x cos2x + 3 = (x - 2)² using Newton-Raphson Method and an intial value of 1 with an error…

A: The given problem is to find the approximate root of given equation using newton raphson method with…

Q: 9 coshx - 5 sinhx = 15

A: Note the following result : cosh x=ex+e-x2  sinh x=ex-e-x2 . In above formula , x∈ℝ . To solve the…

Q: The integration expression sin(3In(x)+ 4)cos(3ln(x)+ 4)dx must be transformed into using suitable…

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Q: (b) Prove that : - 1) (coshx)² – (sinhx)² = 1

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Q: 5. Compute Jo Jitvx 1 dx -2

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

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Q: */16 etan(1r) sec2(4x) dr

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Q: Sec-S 2 1 TanOLO

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Q: 3. Apply the Chain Rule and explain the differences among the following four ex- amples from the…

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

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Q: Use the addition formulas to provesinh(2x) = 2 cosh x sinh xcosh(2x) = cosh2 x + sinh2 x

A: Our Aim is to prove the following identities:-(a) sin h(2x)=2 cosh (x) sinh (x)Proof⇒Since, sinh…

Q: Prove: cosh 3x = 4 cosh° x x-3cosh.x

A: Prove that :- cosh 3x=4cosh3 x-3cosh x

Q: Use Newton's method to find the second and third approximation of a root of 3sin(x)=x starting with…

A: Here 3sin(x)=x∴3sin(x)-x=0Let f(x)=3sin(x)-x ∴f′(x)=3cos(x)-1 x1=2 1st iteration…

Q: 4х, th dt Vhat is the

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Q: 7,2 Find the critical noint(s) of al r) and use the Second Derivative Test to classify the

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Q: 2. Solve 3shn-sinx-2= over the interval [0,27). 2 sın'x-sinx-|:0

A: The objective is to solve the above expression.

Q: Use a linear approximation (or differentials) to estimate the given number.   27.tan 2°

A: The Linear approximation of the function at x=a is given by L(x)=f(a)+f'(a)(x-a) To Find Linear…

Q: Compute ∫xsin(3x−2)dx.

A: Let the given

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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: Evaluate the integral. S sin (7x - 10) dx ㅇ cos (7x-10) +C -cos (7x - 10) + C cos (7x - 10) + C 7…

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Q: (b) Prove that : - 1) (coshx)2 - (sinhx)2 = 1 ,2) coshx - sinhx = e, 3) (cothx)2 -1= (cschx)2 %3D

A: Use hyperbolic  function

Q: How many iterations are needed to obtain the root of f(x) = 3x + cos2x if the bracket is (-0.5, 0)…

A: False position or Regula Falsi method uses the formula below to perform the iterations.…

Q: find the value in terme of x} Z in Boolkan

A: The given problem is to express the given boolean expression in terms of x and z. Given boolean…

Q: Express the first four cumulants in terms of central moments.

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Q: Compute the derivative of y = In ( VI-2 conh z - (z² + 2) -(2- 1)

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Q: Prove sech 2  x =1 - tanh  2x

A: we have to prove: sech 2  x =1 - tanh  2x

Q: biz' dt 2

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Q: sech2(In x)

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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…

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.