Hw) Prove That:- 0 sinhz = log (z+lz*+) e coshz= Loy (2/23) ® Tanh'z = +2 1-2 Examml

Q: Find the indefinite integral.

A: According to power rule of integration .

Q: Find hale reange Sine series Ex 2 (odd fourier sseries) For the function

A: Given function is: f(x)=x, 0<x<π2π2, π2<x<π Here, L=π f(x)=∑n=1∞bnsin(nx), where…

Q: Use Taylor’s formula to find a quadratic approximation of ƒ(x, y) = cos x cos y at the origin.…

A:

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: 2. Evaluate the integral / sin'at dt

A:

Q: Find the indefinite integral using the formulas from Theorem 5.25. (Use C for the constant of…

A: Given:      ∫51+e2xdx

Q: Vx2-a²

A:

Q: Use forward and backward difference approximations of O(h), and a centered difference approximation…

A: Given function is, fx=sinx1+cos Then the forward Oh is,…

Q: 29.Verify that W[xλ cos(μ ln x), xλ sin(μ ln x)] = μx2λ − 1.

A:

Q: Find where ln((1+z)/(1-z)) is not analytic.

A: To find: The region where the function ln(1+z)(1-z)), where z∈ℂ is not Analytic.

Q: 15. Use a suitable change of variables to determine the indefinite integral. [1²cos² (1³) sin(1³)dt

A:

Q: @Hiw/ prove that cosiz=coshz @ Cosh'z -sinh'z=1 @1-Tanhz Sechz D cos hiz-l = cschz COS 3 =- Sinh z…

A: (2) we have to prove that,                                                      cosiz=coshz we know…

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: to tal differential of eind the the り23 function ] 2=e + tan Z= Sin 2.

A:

Q: Use linear approximation or differentials to approximate cos (1.6)

A:

Q: Q2) prove that cosh(x + y) = coshx coshy + sinhx sinhy

A:

Q: Verify the integration formula. S 6 sechx dx = tan-1 (sinh 6x) + C (A) No B) Yes

A:

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) | sec?(e) tan7(0) do

A:

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: 12) S (z* + 2x + 1) dx 3 х2 + 2х +

A: Integration

Q: The measurement of the radius of the end of a log is found to be 16 inches, with a possible error of…

A: Suppose r is the radius of the log with the area of the log is given by: A=πr2 So, we have:…

Q: +Jx² +1) Sinh'x=ln(x+ 2. 1. Cosh-x = In(x+

A:

Q: Prove the identity sinh 2x = 2 sinh x cosh x

A: Prove that: sinh 2x = 2 sinh x cosh x

Q: None Q2) prove that cosh(x + y) = coshx coshy + sinhx sinhy

A:

Q: a 5. Using integration by parts twice, prove that the L (sin ax) %3D s2+ a=

A:

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) | sin(76) sec (cos(7)) dt

A:

Q: Use Newton’s method to approximate an intersection point between f(x) = tan(x) and g(x) = 2x. Use…

A:

Q: 7. To evaluate f-cos X-1 dx, the integrand can be transformed to? 1-sin? x

A: Follow the procedure given below.

Q: (a) Evaluate the indefinite integral (anti-derivative) x°(1+ 2*)® dx by using the substitution u =…

A:

Q: zyć dziedzinę naturalną funkcji f (x) = log (arc + arc cos log, (r- 1) + 2 are sin %3D r+4

A: Given :        fx= logarcsinx-4x+4+arccoslog 12x-1+2

Q: dt

A: We have to find indefinite integral

Q: Prove the addition formula for cosh x given by cosh(x + y) = cosh x cosh y + sinh x sinh y.

A:

Q: 15. ſ sin² 3t cos 3t dt

A:

Q: Hico/ prove Thall Cosh2: - 2 tañ z Sinhz: 1+2 Tanhiz =

A: Since you have asked for a question with multiple sub-parts , we will solve the first three…

Q: Find the arc length: f(x) = (x³ + 5)ž – log x? from x = -1 to x = 3

A: Given:          f(x)=43x3+552-logx2       from x=-1 to x=3   Arc length =∫ab1+f'(x)2dx    here a=-1…

Q: Use the Intermediate Value Theorem to show that 2x – 3 - if – 3 0 has a zero on the interval [-2,…

A: First compute the function if they are continuous then apply the intermediate value theorem.

Q: Example Let sinh(2)e f(2) Find the residue at z = 0.

A:

Q: Use Newton's method to solve for x with an initial estimate of x0 = 2n with d* < 0.001. Cosxcoshx =1…

A: (cos(x))(cosh(x))=1f(x)=(cos(x))(cosh(x))-1ddx((cos(x))(cosh(x))-1)=-sin(x)cosh(x)+cos(x)sinh(x)⇒f'(…

Q: Let the domain of the function f(x) = log4 (log, (log3(18x – x² – 77))) be (a, b). Then the value of…

A:

Q: Evaluate the integral.

A: ∫cosh2(x)sinh(x)dx

Q: = 1. Use a local linear approximation of the function f(x) = ln(x + sinh(x) + cosh(x)) at some point…

A: Since the required point is 0.001 near to 0, so we approximate linearly about x=0, also at this…

Q: B ) if y= sinh¬1x then prove that =

A: Given y = sinh-1(x)sinh(y) = x On differentiating both sides , we get sinh(y)' = (x)'(cosh(y))dydx…

Q: Prove the following continuous time Fourier transform relationship. sin(at) 1 X(N) = Continuous Time…

A: Fourier inverse of XΩ=1    -π≤Ω≤π0    otherwise is : F-1XΩ=12π∫-∞∞XΩejΩtdΩ…

Q: Evaluate the indefinite integral 4(1 + tan(t)) sec2(t) dt Note: Any arbitrary constants used must be…

A: We need to calculate the integral: I=∫41+ tan t5 sec2t dt This integral can be evaluated as follows:

Q: Find differential o perator theit annihilates 4e cos3x+3x2e

A: Given that: 4e2xcos3x+3x2e5x For the differential operator that annihilates the value of f(X) will…

Q: Calculate for one real root of tan x = 4x with xo = 1.2 up to four decimal places using the…

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

Q: I. Verify the following identities: 1. cosh x- sinh x = e* 2. sinh(-x) = –sinh x 3. cosh(-x) = cosh…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: To evaluate the integral cotx log(sinx) dx we use the substitution O a. sinx=t O b. logx=t O c.…

A:

Q: arc sin z = -i log(iz + V1- 22).

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.