1-tanh² x sinh(2x) O cosh(2x) O sech(2x) O csch(2x) O Leave Question O |

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: 8) (10 points) Use Integration by Tables (Appendix B) to find the integral: sin 2x dx 5+3 cos x

A: Explanation of the solution is given below...

Q: Solve Cauchy Euler DE 4x^2y"-4xy'+3y=sin ln(-x), x less than 0

A: Let t =-x >0. Then the differential equation       4x2y''-4xy'+3y=sinln-x becomes…

Q: 8. if y =; sinh(2x + 1) 9. ſ cot* 0 de. 10. * if y = cot-()- tan-1x.

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Q: defines eX-e-x O a. tanh x Оb.csch x O c. sinh x

A: 2ex-e-x=?

Q: Differentiate: y = sinh° (sin 5x) Oy' = 15 cos 5x sinh (sin 5x) cosh(sin 5x) Oy' = –15 sin 5x sinh?…

A: dsinh (ax)dx=a cosh (ax) dsin(ax)dx=a.cos(ax)

Q: 1. Ye = cost- sec(at) %3D ans: =-2sin t - asec(at) tan(at)

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Q: 2 9) -sinh? -cosh -dz

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Q: 5. Calculate the derivatives of sinh¬1x, cosh¬1 x, and tanh¬ x. Hence, express each of the…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: Integral of sin^3 x dx over cos^4 x

A: In this question we have to find the Integration.

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

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Q: undetermint coedticients 11 ON-4y = G²-3) sin x

A: The given problem is to solve the given non homogeneous differential equation using method of…

Q: can you prove it, please ? cosh 2x=sinh^2x+1 = 2 cosh^2-1

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Q: sin(4x) cos(2x) dx = cos (2x) cos (6x)' sin (2x) cos (2x) сов (10х) 4. (2x) sin (10x)+ c sin +c 10…

A: Use formula 2sinAcosB=sin(A+B)+sin(A-B)

Q: 15. sinh 2x = 2 sinh x cosh x %3D

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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: a) y = In x · sinh x*

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Q: 3. Prove that coshx – coshy = 2sinh () sinh ().

A: As per honor code we are entitled to solve only 1 question at a time so I am providing you the same.…

Q: 3. Show that Σ L 1 L-x= 2 2nnx sin L 0<x<L.

A: Let f(x)='12L-x Fourier half range sine series in 0&lt;x&lt;L is bn=2L∫0Lf(x)sinnπxLdx…

Q: 4) coth-lx = .In ( 1+x tanh-11 %3D 2 X-1,

A: i am solving question 4 for other question repost

Q: 1) sinh-1x = In(x + Vx² + 1) %3D 2) cosh-1 x = In(x+ Vx² – 1) %3D 3) tanh-1x In ) X = 1-x

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Q: a)  Use the hyperbolic identity sech^2(x)  = 1 - tanh^2(x)  to solve 4tanh^2 (x)  + sech^2(x)  =3…

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Q: If xy-In(3 sinh(3x)) , then x? y'-

A: Given,           xy=ln3sinh3x

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

A: Given: f(x)=sinh1x2To find:f'(x)

Q: 7. y= (x²-1) sinh (x+1)ª 8. y= sech (1-x³) 9. y =- tanhx

A: Answer (7): The given function is y=x2-1sinhx+14 using product rule in differentiating above…

Q: (ii) Show that 1 d (tanh-1 x) = dx 1- x2 Hence, or otherwise, show that, 27 tanh-1x dx =- In 4 2. 1…

A: Evaluate: and

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

A: Integral of the given function is -

Q: lim (x approaches 0) of [sin(5x)cos(6x)]/(x)

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Q: (5) sinh 2x = 2.sinh x.coshx %3D

A: (5)To prove the following identity sinh(2x) = 2·sinh(x)·cosh(x)

Q: 9. Solve tan x for x where 0<x<90* V3 Enter your next step here

A: Just observe that its value of tan(30°).

Q: SV1+ sin2(x - 2). sin (x – 2). cos (x – 2) dx

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Differentiate: y = ln cosh (cos 2x) 3. O y = 6 sin 2x tanh(cos 2x) %3D O y = 6 sin 2x coth(cos 2x)…

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Q: (3 tanx-2 cos y)sec" xdx + tanxsin yay = 0

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Q: 4. sin 5. y = x ArcCC 1 + v1-x² 2+X 6. y = Arccot x + Arctan 1-2x >| ×

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Q: sin 3x dr + 2y cos* 3x dy = 0 COS

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Q: 1. Prove: a. S csch x = In b. sech x = 2 Arctan(e*) +c ex+1 2. 2e* tanh e* dx 3. S sinh(5x - 1) dx

A: Given : ∫2extanhexdx Let us consider that : ex=u. Therefore, exdx=du. So, ∫2extanhexdx=2∫tanhu.du .…

Q: 9. Find the value of 2sinhxcoshx O a. cosh (2x) O b. sinh(x) O c. sinh(2x) O d. sech (2x)

A: Given:        Value of 2sinhxcoshx     we know that                             coshx=ex+e-x2…

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

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Q: e*+ cos x (d) h(x) = tan x (e) y = Vx sec x e* =dx.secX.さャx.d secxrが4リxのsecX.àビ…

A:

Q: 7. Integral cos x dx sin x

A: This question is related to integration, we will solve it using given information.

Q: 1: Find the derivatives of: 1+ tanh x a) y = In ソ= %3D 1- tanh x b) 2 y= cosh? 1-x? 1-x

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Q: cos x sin x dx 4. sin 2x cos 2x dx 5. cos x sin* x dx 6. sin 3x dx 7. sin³ x cos? x dx 8. 3.

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Q: y = sin(2x) sin(x) + cos ( 2x) cos (x) COS %3D

A: Using the formula of cos(A-B)=cosAcosB+sinAsinB. Explanation is given below..

Q: dx 2 sin x - cOS X |tan+ 2 + V5| In 5 tan; + 2– V5 |tan+2-V5 + C + 2+ V5 2. + C In Option 1 O Option…

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

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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: 15. f(x)= sin 3x 17. f(x)= tan 2.x 19. f(x)= 3 cos (x – 7/2) -

A: 15) For sin(3x) the range of the function will  be the same as sin(x) just the period, in this case,…

Q: 1. lim 3r+2r+1 X-n Sx2+7x+4 2. lim +sinx

A: See 2nd step

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.