5.) y=cot(4(x+))-1

Q: 4. Prove that the equation x + sin(x) = 1 has at least one solution in the interval |3D Va + 3 (0,…

A:

Q: 2.1 Given that sinh x = [e" – e=*] - - show that dy cosh a. da

A: To Determine: show that dydx=cosh x Given: we have sinhx=12ex-e-x Explanation: we have…

Q: Ju

A: To solve the Laplace equation for rectangular plate subject to the given boundary conditions.…

Q: Evaluate the integrals

A: To evaluate the integral I=∫0π/4∫0ln sec v∫-∞2t ex dx dt dv   tvx - space

Q: 1+cscx cotx integralf dx is ec X-CSCX

A:

Q: 2. A particle moves along the parabola y = x in the first quadrant in such a way that its…

A: Given: A particle moves along the parabola y = x2 in the first quadrant in such a way that its x -…

Q: The approximation of xln(x + 3) dx using two points Gaussian quadrature formula is:

A:

Q: If xty= 2e Cos Øand x-y=2ies.m Ø show that Su

A:

Q: -If u = x2 tan-1 २|४ y = - y² tan-1 x 22u дхду x² что - у² + J²u u ә2u u дхду дудх L ala 2

A:

Q: How large should n be to guarantee that the Trapezoidal Rule approximation to | (-x* + 14x³ – 36z² +…

A:

Q: リ=!-Cos2x 1+(os 2x prove y = 2 tanx .secx

A:

Q: first and second derrivative of: y=Arccos(e^2x)

A:

Q: the rocket exploded at the peak of the projectile, part I falls at distance less than d to the…

A: In the given question, the concept of Centre of mass is applied. Centre of Mass The centre of mass…

Q: 1 dy sin¬' x If y = xv1 – x² + sin=1 x, prove that 24 – 2

A:

Q: 9. If y = costhen the second derivative is 5x 25 Cos, 16 5x 5x sin- 4 d. 25 5x sin- 4 a. 25 b. C -25…

A:

Q: 1. If f(x, y)=3x' sin y- y² cos x- 2yln x– xh y- 4xy , find- of ôf ô²ƒ ô²ƒ

A: Given: fx,y=3x3siny-y2cosx-2ylnx-xlny-4xy2

Q: 5. If y= tan x, prove that y``=2(1+ y² )(3+ y²).

A: Prove the given equation

Q: Use trapezoidal with 3 level Romberg ( k=3) to evaluate 1 Пх - Пх* cos dx 4

A: The complete solutions are given below

Q: 2.2 Use the definitions of hyperbolic functions to solve for A and B if: 5e* – 4e* = Asinhx+B coshx

A: Definition used: sinhx=ex-e-x2coshx=ex+e-x2 Consider the given equation as 5ex-4e-x=Asinhx+Bcoshx…

Q: y = 46 tan B3 – 2 = 4¢ tan az – 2 %3D and y = 46 tan B2 +2 = 46 tan æ3 + 2 %3D and hence all the gas…

A:

Q: What do you mean by euler's theorem?

A: Euler’s Theorem is a generalization of Fermat’s little theorem dealing with powers of integers…

Q: (1) If y = sin(tan-x), prove that %3D (1+ x²)?y" + 2x(1 + x²)y' +y = 0.

A: Since you have asked multiple questions in single request.so we will answering only first question.

Q: 4 cos z Evaluate S 16-y2 ydxdydz

A: To solve the given triple integral ∫0π∫04cosz∫016−y2ydxdydz…

Q: 5) What is the maximum value of y = 5 Cos 4x ?

A:

Q: 4. A force of F(x) = x - cos(3x) + 2,x is in meters, acts on an object. Identify the work required…

A:

Q: etanx -25ınttanx=0

A: tanx-2sinxtanx=0

Q: (§5.4, Q42) Calculate So™ f(x) dx, where sin x, x T

A:

Q: 22. Use the Trapezoidal Rule with n = 4 to approximate 1 (x− 1)² dx

A:

Q: 2. An explosion is recorded by two microphones that are 2 miles apart. Microphone M, received the…

A:

Q: Suppose that an initially full hemispherical water tank of radius 1 m has its flat side as its…

A: Given:

Q: then what is y at x=1?

A: We can find y at x=1 in the following steps.

Q: 1. . Use the method of characteristics to solve the first order equation Uz – 2uy with u(x, x) =…

A:

Q: Submit Answer problem 1 oyt of max

A:

Q: 2. The distance between the points (sin x, cos x) and (cos x, -sin x) is: А. 1 В. V2 C. 2 sin x cos…

A: To find the distance between the two points

Q: 2- y = prove that (sin x) = cos x %3D dx

A: Topic:- derivatives

Q: What is the amount of the rotating body formed by rotating the region bounded by the y = cos x…

A: The volume of the solid formed by revolving the region bounded by the curve y=f(x) and the x−axis…

Q: tan st e dt 2

A: “Since you have asked multiple question, we will solve the first question for you. If you  want any…

Q: Compute the length of the curve r-4 sin 26 for Approximate to three decima places.

A:

Q: 8. 4 6° sin°3ycos *3y dy

A:

Q: find do diy y = (cos(x))*os)

A: Given y=(cos(x))^(cosx) Now differentiate y with respect to x

Q: If y= tanu, u=v-- -, and v=ln x, dy at x= e? dx what is the value of

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Q: y"+4y=sin 2x, where y(0)=3 and y'(0)=¾

A:

Q: Suppose the true relationship of Y and X, Z is given by 1. Yi = B1Xi + B2Zi + ei under classical…

A:

Q: The equation, therefore, becomes 6cos x sin y(y') = cos x cos y- sin x sin y(y'), %3D and we need to…

A: Given equation in part 3 is  6cosx-siny(y')=cosx cosy -sinx siny(y') we need to bring all the y'…

Q: 9. Evaluate ſ,(cos x – 1) dx. Tt/2 - π/2

A: topic - definite integral

Q: 26. /(х, у) — х 27. f(х, у) — sin y 28. /(х, у) — х1 + 9у2

A: fx,y=x fx,y=siny fx,y=x2+9y2

Q: Give exomple of o line ar equation s unknown

A: First we see the defination of linear equation then give the answer.

Q: 3 Differentiate: y = In cosh° (cos 2x)

A: As we know that: The chain rule: fgx'=f'gx·g'x The Power law: ddxxn=nxn-1 From the given problem:…

Q: The solution of some second order linear DEQ is exp(-7x)[5sin(1x)+ 7cos(1x)] which can also be…

A:

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.