5. If cosh 2x then the positive value of 4 sinh 2r is

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

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

Q: sinh2 (등)

A:

Q: 1 Show that L-1{ = (sin hat sin at) s4+4a4, 2a²

A: It is given that, L-1ss4+4a4=12a2sinhat sinat. A partial fraction decomposition of ss4+4a4:…

Q: Evaluate sin (44º) + cos (29º) using differentials. Refer to special triangles.

A:

Q: 2.1 Given that sinh x = [e" – e=*] - - show that dy cosh a. da

A: To Determine: show that dydx=cosh x Given: we have sinhx=12ex-e-x Explanation: we have…

Q: Solve the following equation; 2 tanh- 2r = In(r – 2) – In(x). %3D

A: We solve this following equation using simple mathematics and its solve in a simple form of…

Q: Find the indefinite integral. sinh(6 – 7x) dx

A: Consider the integral  ∫sinh(6-7x)dx

Q: 3) Prove that c) cosh2x = 1 + 2 sinh? x

A: In the question we have to prove the given function.

Q: Evaluate the integrals in Exercises

A: ∫-ln20cosh2x2dx∫0ln104sinh2x2dx

Q: Show that (1-)dy+(cos xsin x-sy")dr =0 is an exact equation. Hence, find its general solution. Hint:…

A:

Q: Which of the following is correct? " 17 3 (3 sinh-(x)) = (coth"(x) = (지 < 1) V - 1 dx Option 1…

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Q: 10. Suggest ways to avoid loss of significance in these calculations. (1) Vx² +1-x; (3) sin x- tan…

A: 1 x2+1-x By rationalization  =x2+1-xx2+1+xx2+1+x=x2+1-x2x2+1+x=1x2+1+x Therefore, as x→+∞ there…

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

A:

Q: 7 Express cach of the followir giving only principal values: (a) sin (2 – i)

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Q: Show that coshxt sinhx= ex and coshx- SinhX = e-x, Hen ce deduce cosh?x- Sinh?X=|

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Q: 1) If y = (x-a)√2ax-x² + + a is constant. x- -1(*-ª) ,then y' = 2√2ax - x² a² sin-¹ a²

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Q: 43. If > 2, then -dr = - 4 Jcos (4) + k B sin- ()+ k '(;) + A Cosh- (5) + k cosh=(4 D 2 tanh-(4) +k

A: for this integration, we will assume that x=sec(theta) and from that, we will solve the integration.…

Q: Find the indefinite integral. sinh(4 - 7x) dx

A: evaluate the indefinite integral ∫sinh4-7xdx

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

A:

Q: 16. If 2 sin 2x s 3 cos2x and 0s 2x then x=

A: Given : if 2sin2x = 3cos2x and 0≤2x≤π2 . then we have to find the value of x.

Q: If Z= sinh () show that: *=+y==0

A: GivenZ=sinhyx

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

A: We have to find the value of integral

Q: If x= cos n + cos 2n and y=sin n + sin 2n show that  2xy= sin 2n+2sin 3n+sin 4n

A: See the attachment

Q: Find the indefinite integral. sinh(8 – 7x) dx

A: From the given problem: I=∫sinh8-7xdx  ....(1) As we know that; ∫sinhxdx=coshx+C

Q: Use a calculator to compute sinh x and cosh x for x = −3, 0, 5.

A:

Q: | sinh54x cosh 4x dx can best be evaluated by General Power Formula. A True В False

A: The given integral is ∫sinh54xcosh4x dx. We have to check whether the given integral can be…

Q: 17. If 4 sin x+3 0 on 0 sx < 211, then x=

A: We have to find x if 4 sin x+3=0 on 0≤x≤2π. Solving the given trigonometric equation, 4 sin x+3=04…

Q: Use the hyperbolic identity cosh(2x)= 2 cosh2 (x)-1 to solve 4 cosh(2x)– 22 cosh(x)+ 19 = 0 .

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Q: In( cosh(3x)+sinh(3x) )= Select one: O 3 sinh(3 x )+ 3 cosh(3 x) O- 3x 01 zero None O 3x

A: Formula to be used sinh x = [ex– e-x]2cosh x = [ex+ e-x]2

Q: What substitution should be used to solve the integral O sinu=3x/2 O sec u =2x/3 O sec u =3x/2 O tan…

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Q: 4 sin' 2x cos 4x dx 4.

A:

Q: 2. L{cosh 3t sin 3t}

A:

Q: 22 Evaluate s cos (Iz)e dz

A: Formulae used: ddxcosx=-sinxddxsinx=cosx∫eaxdx=eaxa∫cosxdx=sinx+C By party integration formula…

Q: 15. -- sin(2+ 2) dz

A: According to the given information, it is required to solve the give integral.

Q: 26. If cosh 2z = ° then the positive valuc of sinh 2r is 4 B D com

A:

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

A:

Q: If e/½i =sin2 then z = - 2i In(sin2) + 4k TI 2i In(sin2) + 4k T - 2i In(sin2) – 4kT -2 In(sin2) + 4k…

A: We will find the solution

Q: 4. Evaluate sin (44°) + + COS (29°) using differentials. Refer to special triangles.

A:

Q: 1. f/² sin (1) cos (4) Sir sin (²) dx (Consider initially the first 2 terms)

A:

Q: B ) if y= sinh¬1x then prove that =

A: Given y = sinh-1(x)sinh(y) = x On differentiating both sides , we get sinh(y)' = (x)'(cosh(y))dydx…

Q: 9. Prove that | sin n0/sin 0| <n, limiting values being used when sin e = 0.

A:

Q: In( cosh(11x) - sinh(11x) )= Select one: 01 O 11 sinh(11 x )+ 11 cosh(11 x) O None O zero O-11x O…

A: In this we have evaluate the equation ln(cosh(11x)-sinh(11x)).

Q: 5. Explain in words what the output of sinh (y) geometrically represents. ule

A:

Q: 2. 1 Given: cosh x==(e* + e*), =(e* - e**), use these sinh x = definitions to show that cosh²x-sinh2…

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Q: 3 Differentiate: y = In cosh° (cos 2x)

A: As we know that: The chain rule: fgx'=f'gx·g'x The Power law: ddxxn=nxn-1 From the given problem:…

Q: Find the indefinite integral. sinh(2 – 9x) dx

A: