gives a value of sinh x or cosh x. Use the definitions and the identity cosh2 x - sinh2 x = 1 to find the values of the remaining five hyperbolic functions.1. sinh x = - 3/4    2. sinh x = 4/3

Q: Which of the following is the local maximum value of the function y=(sinx +3) in the interval…

A: Given function , y=f(x)=(sinx +3), x∈0,π

Q: The value of L(e" sinh(3t)) - 3. (-2) + 9 3 (8+2)ª + 9 3 (812) 9 O None of the choices 3 (-2) 9

A: The following Laplace formula are used in solving the given equation. Leat sinhbt=bs-a2-b2

Q: Consider the following. cos(x) + Vỹ = 3 (a) Find y' by implicit differentiation. y'= (b) Solve the…

A: We have to find y' by different method as p[er given in question.

Q: а L {sinh(at)} : given that sinh (at) = So %3D s2 -a? 2

A: This is a problem of Laplace transform.

Q: f sin √x dx

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Q: The value of L(e2t sinh(2t)) =

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Q: ortheangena 24 and y=Sinf)at amything special about h

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

Q: Evaluate the function (a) sinh−1 0 (b) tanh−1 0 . If the value is not a rational number, round your…

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Q: Consider g(x)= {a sin x + b, if x ≤ 2pi} {x2 - pi x + 2, if x > 2pi} A. Find the values of a and b…

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Q: 35. G(t) = sinh(In t) %3D

A: We have to find derivative

Q: 3 Sin 3t-2 cos zt ; s()| こ what B the onti derivative Satifies re conditon is SLE) =>

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Q: x dx x² + √√x². The integral - sine de SSH 1 + cose sece tane de sece - 1 sec²0 do 1+tano cose do…

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Q: Given sinh(r) = then tanh(r) = Select one: a. b. + C. + d. OS Shot by Hisense H12

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Q: fip Find or y' of the following functions and make any obvious simplifications: dx a. Y = arctan(e")…

A: Find derivative of the following using the properties of the derivatives

Q: Which of the following shows finding the area of an area outside the curve Y- 36 sin (20) and within…

A: Please see the attachment

Q: B) If sinh e V3 Find cosh 0, tanh 0, coth 0.

A: The function sinh(θ) is called the hyperbolic sine function. It is defined as sinh(θ)=eθ-e-θ2.…

Q: Express the following function in terms of ‘Sine & Cosine’; y (t) = 4 sin 2πt + 15 cos 2πt

A: Topic- trigonometry basics

Q: d 75. Proof of (cos x) = - sin x Use the definition of the dx derivative and the trigonometric…

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Q: find an antiderivative for each function. Do as manyas you can mentally. Check your answers by…

A: Given function is cosπx2+πcosx. We have to find anti-derivative of given function. Anti-derivative…

Q: e) If the cable of this generator has a shape of the form: y = 70cosh(x/55)sinh²(-) m. Provide fully…

A: e) Given, y=70coshx55sinh2x55m vi) At x=10, y=70cosh1055sinh21055 m=70cosh0.1818181sinh20.1818181…

Q: A value of sinh x or cosh x is given. Use the definitions and the identity cosh?x- sinh²x=1 to find…

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Q: ex+e-x and 2 Given that cosh x %D = ex-e-x sinh x = 2 find the following. a. tanh(ln 2) d b. dx…

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Q: Use the Newton-Raphson to find a root of the equation x' = -cos x. Use an initial guess of x, =1…

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Q: Use the formula for the slope of the tangent line to find of c(0) = (sin(20), cos(70)) at the point…

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Q: If y= sin?t- 2+ + tant, x= – In(- cost) – e sinr, find the value of y when t= (=- 2/3 V2-e 2 6. 2le…

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Q: W (sinh x , cosh x) = ? Select the correct response: O -2 -1 O 1

A: We will find the solution using the given operator.

Q: e* +e* cosh(x) = cosh(0) = ? 33- e* -e sinh(x) = → sinh(0) = ? 2

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Q: Which of the following is(are) true? (Choose all applicable answers.) O coth x = e +ea -e-x cosh x =…

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Q: Fliminate the following. the parameter ) from x(H=2Sint (+)=5 cosf

A: Given, x=2sint        .....(1)y=5cost       .....(2) From equation (1) and (2) sint=x2         ....…

Q: Solve the following with 3 decimal places if necessary. 1.Find L(f) if f(t) equals: i. tcos5t ii.…

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Q: Ex: Find the value of cosh(0) , sinh(0) e° +e0 =1 -0- cosh(0) = 2 e° -e-0 sinh(0) 2 0 =

A: Hyperbolic function

Q: If sinh I = 2 =, then tanh z is Select one: V5 O a. b. y5 2 O c. V5 O d.

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Q: 13. Finally, recall from class that the so-caled hyperbolic sine and cosine functions are defined in…

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Q: If: e = a and ey = b Find the value of tanh(x) + sinh(y) for a = 0.77 and b = 0.35 %3D

A: We will use the following formulas sinh(x)=ex-e-x2,  cosh(x)=ex+e-x2 and…

Q: d (d) Compute (cosh(x)). dx (e) Compute cosh(x)+ sinh(x). (f) Show that the hyperbolic sine function…

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Q: 6. (a) e' sinht (b) 3e2 cosh 4t

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Q: ouse the imProved wmethod Solve the : y ty tan X= sinzX ;ylo)=l ;h=ol

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Q: 22. Given that sinh 2 =, the value of cosh z is A. +- В. D. 4

A: Given: sinh x=34

Q: The height of an arch above the ground is given by the function y = 10 cos x for - 5sxs, What is the…

A: The height is:-

Q: Find the x-coordinate of all points on the curve y = 14x sin (17x) + 119/2x2 + 55 <x< 34 34 where…

A: Please see the below pictures for detailed solution.

Q: Prove the following (sinh x + cosh x)^= e%x cosh?x-sinh?x = 1

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Q: L s²-a? .2. .A cosh (- (at .B (cosh (at .C (sinh (at II

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Q: Which of the following integrals will yield an inverse trigonometric function? e2x dx 4+e2x wdw (B…

A: Let I=∫19-16x2dxI=∫11-16x29dxI=∫112-43x2dxWe know tha…

Q: Using the Taylor's formula calculate cos 9° n=5.

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Q: 8. Which of the following will satisfy the equation below | f(x) dæ = arctanz+C?

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Q: Find two roots for the following equation using Newton-Raphson method: tan x +x-1=0

A: Given function is fx=tanx+x−1. We have to find the roots pf the given function by using…

Q: fip when r = 0, if given y = tan (sinh z). Find dr

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Q: sinh?x + cosh?x= ±et* %3D

A: Given expression, sinh2x±cosh2x=±e±x To prove this in the following.

Q: cosh² x – sinh? g(x) = 1 – tanh?

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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.