10. Compute the following: »TT/4 (a) COS dx 3 (b) dax

Q: For which values of x are y = sinh x and y = cosh x increasing anddecreasing?

A: Hence, sinh x is increasing for all x.

Q: √xA)• dS over the surface of a hemispherical bowl of radius 2 and its circular rim if A = 3 sin(-)â,

A: Please see the attachment

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

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Q: Evaluate the integral. sin 4x cos 9x dx |sin 4x cos 9x dx =

A: topic - indefinite integral

Q: The approximation of I tanx dx using composite Simpson's rule with n=5 is: = None of the choices

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Q: Let 5 sin æ + 6 cos y = 6. dy dx d?y dx?

A: 5 sinx +6 cosy = 6  Differentiating w.r.t x,  5 cosx +6 (-siny) dy/dx = 0  dy/dx = 5cosx/(6siny)

Q: Find integral.

A: We have to find the integral I=∫cos(5x) dx

Q: Find the slope of the tangent line to the curve: 3.) Ħan0 at 0=n/4 4.) sin20 at 0=x/3 5.) rcos20 at…

A: Use the formula for the slope in case of polar coordinate.

Q: 7 show that: sech x dx = Sin (tankx). √1-u² multiply note: * & Sim'u = dx * you Cam سال dx sechx by…

A: Differentiate rhs

Q: 10. Find , if y = dy 1-cosx dx 1+cosx

A: Given  y = (1- cosx) /(1 +cosx) To find dy/dx

Q: Only one of these calculations is correct to evaluate the definite integral V sinx dx Using the…

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Q: (雲) 1 dy tion 1+ is = 3 dx wy da 3, 1 12, 1 1, 15 15, 1

A: We have to choose the correct answer

Q: Use trapezoidal with 3 level Romberg ( k=3) to evaluate 1 Пх - Пх* cos dx 4

A: The complete solutions are given below

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Q: Bind dy, 4. Ssinx.cosx sinx-coSX 1 +2.Ln X

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Q: Use the trapezoidal rule withn= 4 to approximate %3D cos(x) COS

A: Given: n=4 and ∫15cos(x)xdxwe know that trapezoidal rule for approximating ∫abf(x)dxis given…

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: 2. Find the following indefinite integral. et cos cos (3x)dx

A: To evaluate ∫excos(3x) dx

Q: (27 (b) Show that 0. 4 tanh- 2x dx In 8. 16

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

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Q: Use Simpson's rule with n = 6 to approximate %3D cos(a) dx 0.08 Keep at least 2 decimal places…

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Q: f'(t) = sin 8t - cos -/-

A: You are correct

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

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Q: Show that d /dx  arctan ( tanh x ) = sech 2x

A: We have to show that ddx(tan-1tanhx)=sech2x

Q: Compute coshx and tanhx, assuming that sinhx = 0.8.

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

A: Given,           xy=ln3sinh3x

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: Ni cos(2?)a. Cos | x dx

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Q: find dy / dx for Hhe tellowing in (sec EX) In (cosp?}

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Q: Use Simpson's rule with n = 4 to approximate 3 cos(x)

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Q: 4. Evaluate: a) 4 (earctan x)dx o dx b)음 arctan x dx # earctant dt

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: 5. Find where y = In(cosh(2x)) + /sinh-1(2x) + tanh² (7x). dy dx

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Q: Use Simpson's rule with n = 6 to approximate cos(x) rp-

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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: Va2-x² Y=Arc sin + а

A: Differentiate wrt x

Q: Find cosh æ In(sinh x)dx.

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Q: 1. Use the fact that coshx = (e* + e) and sinhx = 1 NIH (ex - e-*) to solve for 1 coshx+ sinhx dx

A: ∫exdx=ex+c

Q: 3. In (cose) tane de

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Q: Integrate (three) of th 1) f sin6x cos3x dx 4) [x² (1+¹)4 dx

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Q: Su+1 dn th-2

A: I =   ∫135x + 1x2 + x - 2dx    = ∫135x + 1x2 + x - 2dxWriting5x + 1  = A (2x + 1) +BOn solving , A…

Q: The answer of integ ra Ssinzx cos3% dX

A: We have to evaluate the given integral.

Q: show that d/dx arctan (tanhx) = sech (2x)

A: On differentiation, we get

Q: Calculate •3 2x -dx et – 1 - -3 by Gaussian quadrature with n = 3.

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Q: Integrate: S dx sin ³x cos6x

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Q: The approximation of 1 = f*cos(x³ - dx using composite Simpson's rule with n= 3 is:

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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: In estimating | cos(4x)dx using Trapezoidal 1 and Simpson's rule with n = 6, we can estimate the…

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Q: integral from 0 to pie over 4 of sin^2 (4x) cos^2 (2x) dx

A: