9 coshx - 5 sinhx = 15

Q: Evaluate y' y = cosh²12x +sinh²6x

A:

Q: find integral of sin-4x

A: Given: -

Q: 101 Jzy cosu(x) + sinh(x)

A: Given differential equation:d2ydx2-y=coshx+sinhxTo find: General solution. Note:1 coshx=ex+e-x22…

Q: Use the definitions of cosh x and sinh x to show that cosh2 x - sinh2 x = 1.

A:

Q: Find the indefinite integral.

A: According to power rule of integration .

Q: Find the upper bound on the error if tan '(2x²) × 2x² and þx|< 0.2

A: In this question, we find the error bound for the given expansion tan-1(2x3)≈2x3 for |x|&lt;0.2 We…

Q: By using the definition of hyperbolic functions, show that sinh x = 1 (cosh 2x – 1). -

A: Given,         sinh2x=12cosh2x-1

Q: Use Newton Raphson method to obtain a root to 3 decimal places :  sinx=1-x

A:

Q: Verify the identity cosh2 x = (1 + cosh 2x)/2

A: We simplify each side using the formula of cosh(x)   Left side:

Q: evaluate the definite integral from [0,pi] [(sinx)2(cosx)4]

A: To integrate the definite integral

Q: Show that coshxt sinhx= ex and coshx- SinhX = e-x, Hen ce deduce cosh?x- Sinh?X=|

A:

Q: Find the upper bound on the error if tan (2x')~ 2x and x< 0.2 -1

A:

Q: Solve for 0 <x< 2n. 4sin'x - sinx = 0 %3D

A: Solution of trigonometric equation

Q: sinh(9x) If g(x) : 8 + cosh(9x) find g' (x) 8+ cosh(0)

A: Following formulae are used to solve first question

Q: +4)° x = sinh4t

A:

Q: f6)= Sin () (x 3x26x-8) 1 CosX In Ceos x) | $66)=Sinx+t Cosx. sinsetl -6()=DSin -2053 2.

A:

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

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

Q: Verify Eq. (2): cosh 2 x - sinh2 x = l.

A:

Q: Use th Start! 1- cos 2x

A: Given:1-cos2x/cos2x To simplify we use some trigonometric properties

Q: FIND THE REAL ROOT OF X.EXP(X) = COSX BY SECANT ITERATIVE METHOD CORRECT UPTO 4 DECIMAL PLACES.

A:

Q: vx +1 Sinh Cschx = In 671 %3D %3D

A: First, let us evaluate sinh-1x.  Let  sinh-1x=zx=sinhz It is known that sinhx=ex-e-x2 Therefore,…

Q: sin 3x• tan 3x

A: Given integral,

Q: 11-­ Use linear approximation to estimate sin29(degree).

A: Given, sin 29° To find: Value of sin 29°using linear approximation

Q: Expand fix)= Sin(x+ TT),O<X< I ina half range sine series

A:

Q: 7. Integrate. S tan50 sec³0d0

A:

Q: : Find value of x if :- 2 sinh (2x) - 4 cosh (2x) = - 4

A:

Q: On the guide to solve integral sin2x/1+cosx why is the first step changing it to 2cosxsinx/1+cosx?

A:

Q: Use false position method to find the root of f(x) = e* (3.2 sin x - 0.5 cos x) on the interval…

A: We need to find the root of fx=e-x3.2 sin x-0.5 cos x The given interval is 3,4 Also, we are…

Q: Find ∫cosh 2x sinh2 2x dx.

A: To find the value of the integral∫cosh2xsinh22xdx

Q: find the root of 3x +sinx -e ^x=0 using secant method

A: Let us consider the function fx=3x+sinx-ex. We have to use the secant method to find the…

Q: Evaluate the integral.

A:

Q: Use the definitions of cosh x and sinh x to show that cosh2 x - sinh2x = 1.

A: To show that cosh2x - sinh2x =1.

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: 3. J sin53x dx. 4. J tan 2x sec22x dx.

A: ∫ax+bn dx=1aax+bn+1n+1+C

Q: If Z= sinh () x- show that:

A:

Q: sin 3xdx Evaluate: S 4+cos?3x

A:

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 calculator to compute sinh x and cosh x for x = −3, 0, 5.

A:

Q: Use Fixed-point iteration or Newton-Raphson method to find the required root. Find the positive root…

A:

Q: Use Newton's method to obtain a root for x^3 - 2x + 5 = 0

A:

Q: sinh 2x cosh 3xdx.

A:

Q: what is -sinh(x) equal when x = 0

A: We know that   sinh(x)=ex-e-x2 Then -sinh(x)=-ex-e-x2 now substituting x=0 in the above equation…

Q: By using siMPSon method find Sinx da for 3(0,25)

A: Given integral is, ∫01sinxxdx With the step value of 0.25. By substituting the step length the value…

Q: Exercises to solve: 1. fx² In(x + 1) dx 2. (x2 + x – 2).cos4x. dx 3. Se-*sinxdx 4. S sinh2x.cosh5x…

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

Q: 2* csch (2*) cosh(2*)-sinh(2*)

A:

Q: Prove (sin10x)/(sin9x+sinx) = (cos5x)/(cos4x

A: Explanation of the prove is given below..

Q: Evaluate the definite integral. 1 cosh24x sinh 4x dx

A: Note that the following results are to be used for the given question: (i) sinh x=ex-e-x2 (ii) cosh…

Q: In( cosh(3x) - sinh(3x) )=

A:

Q: Q3: Find 1. cosh(5x)+ sinh(5x) 2. (sinhx+ coshx)*

A: Given,

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.