What does the "prime sign" mean in h'(w) ? What does the "prime sign" mean in p'(y) ? What does the "prime sign" mean in N'(k) ?

Q: Separate tanh-1(x+ iy) into real and imaginary parts.

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

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

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: Integrate sin^2(7x)-cos(x)

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Q: (b) Prove that : - 1) (coshx)2 – (sinhx)2 = 1 ,2) coshx- sinhx = e-*, 3) (cothx)? -1= (cschx)?

A: Given that  The following

Q: EX / Show that cosh x-sinhx=1

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Q: How would I approach this problem algebraically, and analytically? I have attached a photo.

A: To find:

Q: 2. Find the root of the function using Fixed-point Iteration. f (x) = x cos (x) - x?

A: Consider the given function as, fx=xcosx-x2

Q: Express in exact form: In(x² + 1)dx

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Q: In estimating cos(3x)dx using Trapezoidal and Simpson's rule with n = 8, we can estimate the error 1…

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Q: 3 In estimating | cos(5x)dx using Trapezoidal and Simpson's rule with n = 8, we can estimate the…

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Q: 1- Prove that cosh 2x - sinh 2x = e2

A: sol)Given cos h 2x-sin h 2x=e2x

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

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

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Q: Jse differentials to approximate 47. (Express as a rational number.)

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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: In( cosh(7x) + sinh(7x)) + In( cosh(7x) - sinh(7x) ) =

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Q: Show that Costy+ Co5' (-x ) = TT.

A: To show that the given identity is true,

Q: In estimating cos(3x)dx using Trapezoidal and Simpson's rule with n = 4, we can estimate the error…

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Q: 4) What integrals lead naturally to inverse hyperbolic functions?

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Q: 4. Show that sinx can be approximated by x-x³/6 within 0.01 on the interval [-1,1].

A: see my solution

Q: In estimating cos(5x)dx using Trapezoidal and Simpson's rule with n = 4, we can estimate the error…

A:

Q: dervivative of (ln(cosh(x)))3

A: Given data:     The given function is: y=(ln(cosh(x)))3. STEP-1 Assume u=coshx and differentiate it…

Q: he measurement of the radius of the end of a log is found to be 20 inches, with a possible error…

A: Given that: Radius of log, r=20 inError in measuring radius, dr=18 in

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

A: Given,           xy=ln3sinh3x

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

A: Here we will use the relationship betweencosh2x and sinh2x to find the value of sinh2x from the…

Q: Use differentials to approximate the value of <2.1.

A: Given  Find the value of 52.1

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

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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: 7. To evaluate f-cos X-1 dx, the integrand can be transformed to? 1-sin? x

A: Follow the procedure given below.

Q: In estimating | cos(3x)dx using Trapezoidal and Simpson's rule with n = 8, we can estimate the error…

A: We have to find the error in trapezoidal and Simpson rule .

Q: Use differentials to approximate the value of (2.001)’.

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Q: Compute the fourth derivative of cos(x+1) - ln(x²+4) + x²²+1 with respect to x. Also, compute the…

A: Sol:- First part:- Fourth Derivative of given function:-…

Q: 9. tan 4x sec24xdx d. cos 5xsin 5xdx e. x sin(3x² +1)dx f. [x* cos(2x' +1)dx

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Q: In estimating cos(5x)dx using Trapezoidal and Simpson's rule with n = 6, we can estimate the error 1…

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

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.

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Q: 3. In (cose) tane de

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Q: 3:Use Gamma & Beta properties to evaluate : f (In x)³ dx

A: The gamma function is Γ(z)=∫0∞e-ttz-1dṭ The Gamma function is a non-integer generalization of the…

Q: Use differentials to approximate radical (48.7)

A: Ne need to approximate √48.7 using differentials.

Q: 3. Use Simpson's rule to calculate x² sin x dx to within 2 × 10-5 of the exact value.

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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: cosh(In x) dx

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Q: Find the indefinite integral. sec 3x tan 3x dx

A: Given integral, ∫sec53x tan3x dx

Q: 7. Find the first 2 iterations for the root of f(x) = x- cosx by the Secant method on [0,1.

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Q: In estimating : cos(4x)dx using Trapezoidal and Simpson's rule with n = 4, we can estimate the error…

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Q: Evaluate ax xm-1 sin bx dx in terms of Gamma function. -ax

A: We use the special results of Gamma function to solve this problem as in next step.

Q: Compute cosh(x) and sech(x), assuming sinh(x) = 0.01. cosh(æ) = %3D sech(x)

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Q: Use differentials to approximate tan (43°). Round to 4 decimals.

A: Approximate to tan(43°) using the differentials ,