Hico/ prove Thall Cosh2: - 2 tañ z Sinhz: 1+2 Tanhiz =

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: 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 using the appropriate method or combination of methods.

A: Use 2sinA*cosB=sin(A+B)+sin(A-B) formula

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: Estimate the root of 2 cosh x sin x 1, using the secant method, with an accuracy of 4dp. Take 0.4…

A: Image is attached with detailed solution.

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

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

Q: Find the indefinite integral.

A: According to power rule of integration .

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

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Q: Use Newton Raphson method to obtain a root to 3 decimal places 1.   x^3-5x+3=0 2.   sinx=1-x

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Q: f(x)% 3D tanh In(2x) is equivalent to

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Q: 2. Evaluate J dx (cos³x sin³x)

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Q: Use Simpson's rule with n = 4 to approximate cos(x) dx 1

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Q: Evaluate the integral. ∫0 π/2  Sin2 x Cos 2 x dx

A: Consider the given integral as Use the identity to solve the integral such that

Q: y" + y = 3x sin x

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Q: S cose de 1-sine sece tane de sece - 1 The integral fo fse Si x dx x²+√√√x²−1−1 sino de 1+ cose…

A: we have to above integration

Q: limit x to 0 sin(4t)sec(1000t)/10t

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Q: 1 dy sin¬' x If y = xv1 – x² + sin=1 x, prove that 24 – 2

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

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Q: ... at verifies the identity. OC. B. sin 9x cos 7x - cos 9x sin 7x = sin (9x – 7x) = sin 2x sin 9x…

A: Given query is to find the correct option to prove the identity.

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: 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: Integrate this item using (parabolic) Simpson's rule, with interval width of 2.00 units. x tan x + 5…

A: The formula for Simpson's rule isSn=∆x3f(x0)+4f(x1)+2f(x2)+4f(x3)+...+4f(xn-1)+f(xn) where…

Q: Q2- Show that, 2 sin x |Jo(x cos 0) cos 0 d0

A: We have to prove sinxx=∫0π2J0(xcosθ)cosθdθ                     (1) Since we know…

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

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

Q: 3 ven sin(0) = for <<m << then cos(

A: Topic:- trigonometry

Q: A rectangle is to be inscribed under the arch of the curve y = 4 cos (0.5x) from x = -π to x = π.…

A: Consider the given function y=4cos0.5x

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

A: We have to find the value of integral

Q: Differentiate: y = In cosh (cos 2) O y' = 6 sin 2z tanh(cos 2z) y' = -6 sin 2a coth(cos 2x) Oy = -6…

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Q: Use Newton's method to approximate a root of the equation 4 sin(x) = x as follows. Let x₁ = 2 be the…

A: answer is in next step

Q: Evaluate the definite integral. ∫(lower bound=π/4)(upper bound=0)sin(4t)dt

A: Given,             ∫π40sin4tdt

Q: Find a real root for x tan x+1 = 0 using Newton Raphson method.

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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: 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: 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: The integral O cose de 1-sine sec²0 de 1+ tan sece tane de sece - 1 S sine de 1+ cose x dx can be…

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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: Find the x-coordinates of the points of inflection of k(@) = sin (e) on the interval 2 Use exact…

A: h(θ) = sin2(θ)  [ -π/2, π ]

Q: 3 In(1+ V sin²x .limr→0 V1– cos x

A: Consider the given expression. limx→0ln1+sin2x31−cosx Put the limit in the expression.…

Q: S cos (2x) sin* (2x)dx a.

A: Solution: The objective is to evaluate the integral

Q: Solve the integral. cos x dx J (1+ sin² x) arctan (sin x) 10.

A: To evaluate:                      ∫cos x(1+sin2 x)arctan(sin x)dx    ... (1)

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

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

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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: noitutitaduz ontemonoghtanie sin' x dxsldsinsvlenigito adi to amal cos x

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Q: Evaluate integral 0 to pie sin 2 x cos 4 x dx

A: To Evaluate the integral given below:-I=∫0πsin2(x)cos4(x)dx

Q: Find all solutions to cosh z = i sinh z.

A: To find all the solutions of the below equation. coshz=isinhz

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

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Q: 4. Use Secant method with p =1, p =1.2 to find the root of f(x)= Inx – cosx that is accurate to…

A: Given, fx=ln x-cos x; p0=1; p1=1.2; As it is known that the secant method is given as,…

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.