Verify the identity sinh(x + y) = sinh x cosh y + cosh x sinh y

Q: Use the addition formulas to prove sinh(2x) = 2 cosh x sinh x cosh(2x) = cosh2 x + sinh2 x

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Q: A-f cos (x)sin³(x)dx e*cosh (3x) B-J cosh(x)+sinh(x)

A: Here we use use substitution method to evaluate the given integral.

Q: (sech°x)/1+ sin? if y = dx dy Find tanh°x

A: Given:-       To find:- dy/dx

Q: Differentiate the function. y= ln(x3 sin2 x)

A: First, we simplify the given function using the multiplication and power rule of logarithm.

Q: In( cosh(9x) - sinh(9x) ) - In( cosh(10x) + sinh(10x) ) = Select one:

A: Solution: The objective is to find the value of the given expression

Q: dx sinh x - cosh x

A: To Evaluate: ∫dxsinhx-coshx Concept: i. ∫afxdx=a∫fxdxii. ∫exdx=ex+C

Q: Use the addition formulas to prove sinh(2x) = 2 cosh x sinh xcosh(2x) = cosh2 x + sinh2 x

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Q: (7) coshx + sinh x = e* %3D

A:

Q: Integration of (Sin(x) + Cos(x))e^x is_

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Q: Prove: sinh(x – y) = sinh(x) cosh(y) – cosh(x) sinh(y)

A: The basic relations we need to know to solve this problem are, sinh(x) = ex- e-x2cosh(x) = ex+ e-x2

Q: aluate 9/ sin(x) cos(x) dx by four methods.

A: Here we want to perform the given integral according to each of the methods mentioned.

Q: 1. Differentiate the function. y = In(VT sin-(5æ))

A: As per our guide lines we can answer only 1 question. Kindly post the other question seperately.…

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.

A:

Q: Verify the identity sinh x + cosh x = ex

A: To prove the identity

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: sinh x + cosh x)ª= e4x

A:

Q: Prove the identity. cosh(x) + sinh(x) = e* cosh(x) + sinh(x)

A: The solution of the problem is given in the next step.

Q: Verify the integration formulas ∫sech x dx = tan-1 (sinh x) + C

A: To evaluate ∫sech x dx

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

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

Q: Find the solution of (tan x – sin æsiny) dæ +cos xcosydy = 0

A:

Q: Find the first derivative of y = arctan [ (3 sin x) / (4 + 5 cos x) ] and y = ( ex – e –x ) / (ex…

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Q: (A) Prove that: cosh x + sinh x = e*

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Q: Differentiate the function y=ln(x5 sin2 x)

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Q: Verify the identity. sinh2 x = (−1 + cosh 2x) /2

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

A: Integral of the given function is -

Q: Verify the identity cosh 2x = cosh2 x + sinh2 x

A: we have to verify the identity: cosh(2x)=cosh2x+sinh2x   L.H.S: cosh2x as we know that coshx=ex+e-x2…

Q: antiderivate of y = sin x + 6x2

A:

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

A:

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

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Q: Differentiate with respect to x. Y=sin5x

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Q: 3. sin 8x cos 8x dx s 2x sin 2x dx cos

A:

Q: 3. Prove that: cosh x - sinh x = e¯*

A: Proved Coshx - Sinhx = e-x

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

A:

Q: Use sin 0 = 0, sin = 1, and sin t = 0 to estimate sinl E) (Round your answer to three decimal…

A:

Q: dx sinh x + 2 cosh x

A:

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

A:

Q: None c) cosh x + C sinh x +C 2 sinh x +C cosh x +C

A: The given integral,      12∫ex-e-xdx

Q: Find the first derivative of  y = cos4 x – sin4 x y = x3   –  x2 cos x  +  2x sin x  + 2 cos x y…

A:

Q: cos (5x)cos (3x) dx cosh' (In x) sinh (In x) (A) (8) - (C) 0 (D) 2 1

A:

Q: 4 cos °x sin x dx 3x sin: 1/3

A:

Q: differentiate the function: y= ln(x^9 sin^2(x)) y'(x)=

A: Given function as

Q: Prove that cosh(x±y) = cosh x cosh y± sinh x sinh y.

A:

Q: Prove the identity (cosh x + sinh x) n  = cosh n  x + sinh nx

A: Consider the given L.H.S of the given identity coshx+sinhhxn

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

A:

Q: Arc lenght of Curue y=ln(sinx) at intervol I sxS Ę

A: Thanks for the question :)And your upvote will be really appreciable ;)

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: Verify that sin(x+y)+sin(x-y)=2sinxcosy

A:

Q: Prove the identity.   sinh(x+y) = sinh x cosh y + cosh x sinh y

A: To show that sinhx+y=sinhx coshy+coshx sinhy

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.