5 If cosh(2x) = 2 , x < 0 , find the exact value of tanh(x). Enter an integer or a fully reduced fraction such as 4, -16 , 3/7 , 1/9 etc. No spaces please

Q: 9. cosh x + sinh x= e* %3D

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Q: V3 B) If sinh 0 Find cosh 0, tanh 0, coth 0. 2 = %3D

A: Given,  sinhθ = 32  We have to find coshθ, tanhθ  and  cothθ.

Q: 9. cosh x + sinh x = e* %3D

A: To Prove,                cosh x+sinh x=ex

Q: integral of (e^tan(sqrt of x))/(sqrt of x)(cos^2)(sqrt of x)dx with an upper limit of pi^2 and a…

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Q: 1. Write an expression for the evaluation of the integral sin x² dx by the trapezoid rule using n =…

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Q: V3 B) If sinh 0 Find cosh 0, tanh 0, coth 0. %3D 2

A: We are given with sinhθ=32. We need to find some other trigonometric functions. Use the relation…

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: 2. True or False. The dx [Arctan(tan x)] = 1 for all x in the domain. ans. True

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Q: What number a>0 makes it that the area under the function f(x)=sin(2x) between x=0 and x=a is 1

A: The area under f(x) and between x=0 and x=a is given by: Given that this equals 1.  We have to…

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

A: 2ex-e-x=?

Q: use this to evaluate /x*sin (2x)dx

A: Integrating using by parts...

Q: sech (In x*) 15. dx x/6 tanh (In x2) – tanh? (In x2)

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

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Q: Find all values of x in the interval [ -pi/2, pi/2 ]at which the fuction f(x)=sin^2+cos x reaches an…

A: To determine the absolute minimum value of the function.

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: Solve the integral. sech x tanh x 9. 9 + sech? x

A: Given integral is I=∫sech x tanh x9+sech2xdx   Substitute sech x=t sech x tanh x dx=-dt Integral…

Q: Use the addition formulas for sinh x and cosh x to prove tanh u + tanh v tanh(u + v) = 1+ tanh u…

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Q: sech? (In x²) 15. f x/6 tanh (In x²) – tanh² (In x²) dx

A: I = ∫ sec h2 (ln x2)x6tan h(ln x2)-tan h2(ln x2)dx=∫ sec h2(2ln x)x6tan h(ln x2)-tan h2(ln x2) dx=∫…

Q: 4. Interval 0<x<n, function, f(x) = sin 2x. %3D

A: We have to find the Fourier series of the function fx=sin2x ,x∈0,π

Q: 8.) k(x)=-2 tan(2(x+)) Period = Increment =

A: Given function is: kx=-2tan2x+π8 Then the period of this function is 2π2=π. The increment is π8.

Q: ..LH.S.-R.H.S. - HW/ Prove that: (1) 1-tanh x=sech'x

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Q: 3-f(x) = tanh¯1(cos(e*))

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Q: 3. sin(3x) = 3s in x – 4sin³ x

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Q: If f(x)=tanh^-1 square root x to the fourth power then f'(x)=

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

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

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: 5. Express lim 2 cos as a definite integral, then find t

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Q: If sinh x = find tanh x, and sech x. 12' tanh x= (Type a simplified fraction. sech x= (Type a…

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Q: 10. S(tan x – 1)²dx

A: Topic:- application of integration

Q: ph of y = cos x from x = 0 to x = 27 by making a table using multiples of #/2 for x. y= cos x 2 EIN

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Q: 3 tanh (In(4x)) sech" (In(4x)), I) y = tanh (In(4.x)) [y

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

A: Given: sinhθ=32 To find: coshθ, tanhθ, cothθ. Solution: We have identity, cosh2θ-sinh2θ=1 Putting…

Q: 6. Approximate the real root of x – cosx = 0 to three decimal places. Let xo = 0.8 and find x1, x2,…

A: Let f(x) = x - cos(x) x0 = 0.8 By using the Newton-Raphson method to approximate the root,…

Q: 1-sin x F(x) = S₂₁² 5tdt

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Q: dr =ズ Sin )=s OP Type a a exact awser Using X as needed

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Q: 1 + X tanh (x) 1 In 2 - 1 - X

A: The solution is given as

Q: 1– tan(*,) [1– sin x] lim 1+ tan(x (¥2) [z – 2x] x- - 2 1/8 1/32

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Q: tanh(x) = 3/5, find the values of the other hyperbolic functions at x.

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

A: Note: since you have posted multiple questions. As per our guidelines we are supposed to solve only…

Q: 1. cosh (j) 2. tanh 3. 3. In(2 + j3)

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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: S lim 1 (1+x)2+n³ cos (nº + x³) dr

A: HINT:  Used Integration formulas and limit formulas.

Q: 1+ tanh x e 2x 1- tanh x

A: Prove the following Use the identities

Q: k. f(x)=cosh(x³)+ sinh(10x) 1. f(x)=In(x* +1)

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Q: Find 2 sin(x + sin(x + sin a)) – 2 cos(cos 1) lim 2x – T ithout using L'Hôpital's Rule.

A: