1 y = [cosh(2x)]°or¯*( cot-1 3 VX

Q: Find y′ if y = tanh−1(sinh x2).

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Q: s sec(cosx) dydx siny

A: Given : ∫01∫sin-1yπ2 sec2(cosx)dydx

Q: 3. J sinh(5x – 1) dx

A: Please refer the attached image for complete solution.

Q: (sech°x)/1+ sin? if y = dx dy Find tanh°x

A: Given:-       To find:- dy/dx

Q: Use the trapezoidal rule with n = 5 to approximate 3 cos(x) -dx Keep at least 2 decimal places…

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Q: .3 Cos x + cos x dx Vsin a 3,

A: Given…

Q: arccos 2x dx 3.

A: We will use integration by parts. The solution is given below.

Q: Evaluate sin (Inx) dx Integration by parts will be used repeatedly. What is the expression after the…

A: We have to find ∫sinln(x) dxWe will apply formula for integration by parts.We know, ∫uv dx…

Q: 1) [(sinh 2x + cosh2x)° dx

A:

Q: 4(sinh 5. Evaluate 6 x) dx V1+x?

A: We use the well known formula for sinh^-1(x) = ln(x + sqrt(x^2+1)) and then integrate the…

Q: Integral of Sin^2(2t)cos^2(2t)dt

A: Given: ∫sin22tcos22tdt

Q: 28. Se cost sin 2t dt

A: ∫0πecostsin2tdtSolution :∫0πecostsin2tdt2∫0πecostsintcostdtlet, cost=x-sintdx=dxsintdx=-dxat…

Q: Integral from 0 to 2pi of sin(2x) dx

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Q: Evaluate the following integral sec(VT) tan(V7) dx

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Q: 1. S sinh ) dx 2. S sech? (x - ) dx 3. [6 cosh (- Inx )-) dx

A: Since you have posted multiple subparts question in this question so I have solved first question as…

Q: Using secant method, detemine a root of sin Vx - x with initial guesses xo = 0.5 and x, = 1…

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Q: Integral from 0 to pi/2 of (cosx) /(sinx) ^(1/2) dx

A: we have to find definite integral of f(x) in [0,pi/2]

Q: S) - aresin 2. 2 arcsin 2. is constant for 0sxs 4.

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Q: Solve : dy + Sec x tany=D0 /6

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Q: Find ∫cosh 2x sinh2 2x dx.

A: To find the value of the integral∫cosh2xsinh22xdx

Q: | cos (nt)sin(at) dt Find

A: This integral can be solved by the method of substitution.

Q: Tutorial 14 If y = (sin-1 x)², show that dy (1 – a²) - dy = 2. dx dx?

A: Given, y=sin-1x2 Differentiate with respect to x y'=2sin-1xddxsin-1x=2sin-1x11-x2y'=dydx=2sin-1x1-x2…

Q: Find dy/dx given that 3(x +y) = 100xy Solution:

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Q: A frictionless spring with a 8-kg mass can be held stretched 0.8 meters beyond its natural length by…

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Q: +2 dy x2 + sinx – y = 0 dx

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Q: Find the approximate surface area of a sphere of radius 5.02 cm. (SOLVE BY USING DIFFERENTIAL…

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Q: Differentiate y= 3-carhx tespect to X 6+ Sinh x

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Q: 05 (show resulting de) dy x sin x dx cscy

A: Given; dy/dx = x2sinx/cscy.

Q: 6. In(x*y?) %3D х* +уз 7. У- Arccos(e2x)

A: Given In(x3y2)=x2+y3y=cos-1(e2x)we need to find the second derivative of the given equation

Q: sin“ (x)dx 4

A:

Q: (3 sin y – 5x)dx + 2x² cot ydy = 0

A: Given the differential equation:       (3sin y-5x)dx+2x2cot y dy=0 Solve using substitution method.

Q: Sinhx cosy dx = coshx siny dy

A:

Q: Explain graphically why there is no solution to cosh x = sinh x

A: cosh x = sinh x. We need to explain graphically why there is no solution to the given equation.

Q: 5 8. fcscz x cot3 x dx

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Q: Differentiate y= arctan sinh x. coshx A. 1-sinh x cosh x B. cosh x C. ainh-x D. 1+sinh-x

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Q: Find the root of the equation Cosx-x' = 0 near to 0.5 using Newton-Raphson method correct up to 3…

A: To determine the root of an equation using Newton-Raphson method, first choose an initial value x0…

Q: 1. Find y" when sinx + siny = 1.

A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the…

Q: 1. [cosh(x)] = sinh(x) dx

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: find the most general antiderivative or indefiniteintegral. You may need to try a solution and then…

A: We have to find and check the answer by differentiation of the indefinite integral: ∫-sec2 x3dx…

Q: integrate 1/(sin^2(3x) dx

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Q: X= sin 2tS In %3D Find dw 2- Cost

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Q: calculate the integral.

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Q: Particular Intecral for the differen tial equation (0+0ly=Sin k is given by . * COSX * Sinx Sinx D0.…

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Q: 10.y = Arc cot (sinh3x) 11. y = cosh?4x - cos 12. y = In (sinh4x) cosh8x +x² 2

A: To find dy/dx: 10.y = arc cot ( sinh3x ) dy/dx = [1/(1+sinh23x) ]( cosh3x) 3  = (3 cosh3x) /…

Q: dy + y - Sin X dx =0 difference Ekact Solve.equation by

A: The objective of the question is solve the equation of difference.

Q: y

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Q: What is the antiderivative of sec2(5x)dx from pi/20 to -pi/20?

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Q: Show complete solution. Determine the slope of the tangent line to the graph of the equation ey =…

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