For which values of x are y = sinh x and y = cosh x increasing anddecreasing?

Q: Compute cosh x and tanh x, assuming that sinh x = 0.8.

A: Here given as sinhx=0.8 Use the identity…

Q: a if y = In (sinh 50) and x = 7. cosh 40

A: We have given y and x and we have to find out dy/dx

Q: ЗсoshЗx dx| 4 + sinh3x 1/3

A: Given: 13∫3cosh3x4+sinh3xdx

Q: sinh x dx 1+ cosh x

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Q: Evaluate S sinh x cosh x dx by introducing u-sinh x

A: Given that: ∫sinhx.coshx.dx

Q: 14. S 5 sin 3x cos 3x dx 15. ſ tan? Ode

A: We can solve the given integral as follows:

Q: 2. Evaluate the integral / sin'at dt

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Q: Consider the function y = sinh 2x + 1. Which ?one is a critical number of this function

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Q: B. Eind y by implicit differentiation. A.e sinh x+ In y cosh x= tanh(x - y)

A: The given equation is eysinhx+lnycoshx=tanhx-y. Calculate the value of y'. Here we use the formula…

Q: L(cos(at)sinh(at))

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Q: 4(sinh 5. Evaluate 6 x) dx V1+x?

A: We use the well known formula for sinh^-1(x) = ln(x + sqrt(x^2+1)) and then integrate the…

Q: Evaluate S sinh x cosh x dx by letting u=cosh x

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

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Q: 2. Given: cosh x==(e²+ e*), sinh x=(e-e), use these 1-1/1 definitions to show that cosh’x−sinh’x=1.

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Q: Find the indefinite integral ∫cosh2 (x − 1) sinh(x − 1) dx

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Q: Given: 4 2 y = -arctan sinh 3 х — find y' at x = 2 - cosh 1 - y 1 + sinh? 1 %3D cosh 1 y = 1 + sinh…

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Q: 3. Show that sinh a + sinh y = 2 sinh cosh %3D

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

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Q: 9) If f(x) = sinh() , then f'(x) = %3D (A) 3 cosh(÷)

A: Given: f(x)=sinh1x2To find:f'(x)

Q: Evaluate the integral.

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Q: Find the most general antiderivative of the function. f(x) = 5 cosx-7 sinx

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Q: Q4: To evaluate the integral cos x dx using the reduction formula of cosine function

A: We know that reduction formula for  ∫cosndx=1ncosn-1(x)sin(x)+n-1n∫cosn-2(x)dx Now we will solve…

Q: Find sinh + C sech V5 + C sinh () + C X. Cosh 5 O -1 csch--

A: Integral of the given function is -

Q: Find the surface area of revolution of 7 cos(5θ ) between - π/10 and  π/10, about the x-axis using…

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Q: Describe the method used to integrate sinm x cosn x, for m even and n odd.

A: Method to integrate sinmx cosnx ,for m even and n odd. Let m=2k and n=2k+1 ∫sinmxcosnx…

Q: Find the indefinite integral ∫sinh(1 − 2x) dx

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Q: 8. The value of f sinh* x cosh³ x dx

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Q: Find , if y = x sinh x - cosh x %3D dx

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Q: Differentiate y= 3-carhx tespect to X 6+ Sinh x

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Q: Find the indefinite integral. S sinh (1 – 2x) dx

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Q: What is the derivative of y = 10sin 5x 5 In 10 cos x 10in 5x 5 In10 (10sin Sx) A. C. 5 cos x In 10…

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Q: Show that coshr+ sinh a = e and cosh r- sinhr = e. Hence, deduce UTMOU cosh r- sinh z = 1.

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Q: Find for the following functions: (4) y = x sinh 2x --cosh 2x (2) y = tan³√/cot(7x); (3) y= sin Imvr

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Q: Explain graphically why there is no solution to cosh x = sinh x

A: cosh x = sinh x. We need to explain graphically why there is no solution to the given equation.

Q: Find the length of y = ln (sec x) between x = 0 to x = π/4.

A: you meant to find the arc length of y=ln(secx). the formula for the length of the arc in the given…

Q: Differentiate y= arctan sinh x. coshx A. 1-sinh x cosh x B. cosh x C. ainh-x D. 1+sinh-x

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Q: S tanʼx dx

A: Answer is given in next step.

Q: Q3 : prove that : cosh?x + sinh²x =coch2x

A: L.H.S.:=cos h2x +sin h2x=(cos hx)2 +(sin hx)2  =ex+e-x22+ex-e-x22=14(ex+e-x)2+(ex-e-x)2

Q: 1. [cosh(x)] = sinh(x) dx

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: calculate the integral.

A: Given integral is We will use the following substitution to evaluate the integral

Q: Evaluate the integral. sinh 5a -dx +C. 5x

A: Evaluate the integral the given function Sinh is hyperbole function.

Q: Integrate: cos Gx) – sinh(2x)]g

A: As per our guidelines only one question can be answered.Please repost the next part in next…

Q: 2 sin x f(x) = 1+2cosx 5. Pvaluated at x = 1 rad

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Q: Q2): If sinh(x) =find tanh(4x). %3D

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Q: B) Prove that: cosh (x + y) = coshx coshy + sinhx sinhy %3D

A: We know that cosh(θ) = eθ+e-θ2sinh(θ) = eθ-e-θ2

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: What is the derivative of y = 10sin Sx 5 In 10 cos x 10sin Sx 5 In10 (10sin Sx ) A. В. C. 5 cos x In…

A: Given: y=10sin 5x To Find: The derivative of the given function.

Q: Compute cosh(x) and sech(x), assuming sinh(x) = 0.01. cosh(æ) = %3D sech(x)

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Q: Find when 4= SINX Thuen dy (sinx) (ar f(s wheve for 0<x< M2 tanx taux a=?

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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.