Derive y = e*+1 sin x³,

Q: Find a result by using undetermined coefficients for ý + y = x² + x+sin(2x)

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Q: Find tan-1 x2 -dx using integration by parts.

A: Integral by parts

Q: tan Find -dr using integration by parts.

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Q: Show that J (x) = 2 sin x

A: By definition,                  . Now,  we need to prove the above statement by taking n = 1/2.

Q: The y' of the given function is (1–2 sin? 4x) y

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Q: Differentiate y = In (cos² 3x).

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Q: S(sinx – cosx)²dx COoSx

A: Given, ∫sinx-cosx2dx  We have to find the integral.

Q: Find the third derivative of y3= A 1/2 B -5/2 15 D -1 8

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Q: y = 2 sin 3x 1+3 cos2x

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Q: Vtan XP sin X cosX

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Q: Sohe nin(x+y) + cos(x+y) Solve = sin

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Q: Express (cos(20)+i sin(20))*in exponential form

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Q: Simplify 3π2 sinh (πx) - π2 cosh (πx) - 3 sinh (πx) + cosh (πx) = 0 on the interval (0,1).

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Q: The derivatives of sin- 1 x and cos- 1 x are negatives of each other.

A: From the question it's not clear, what do you want us to do with it. I assume that you want to know…

Q: Find /e2x sin(2x)dx

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Q: /2 sin aVT-2 cos r dr /3

A: To find the given integration

Q: #4 tan lun sec x dx 4.

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Q: 7/4 (sec² x – sin x)dx

A: 1. ∫sec2x dx=tanx 2. ∫sinx dx=-cosx 3.∫(u±v)dx=∫u dx±∫v dx 4. ∫abf(x) dx=F(b)-F(a), where ∫f(x)…

Q: DIFFERENTIATE THE GIVEN y = x² co sec™ 3 -1 * COS

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Q: Show that the equation tan(x)=1−x has a real solution.

A: Using Newton raphson method.

Q: y = (cos(3x))*

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Q: y' = 2 - sin t

A: Given that y'=2-sint. solve the above differential equation as follows.

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: xV1- cos x dx

A: ∫0π2x1-cosxdx

Q: f(x) = cos3(4x-1) Differentiate the equation

A: Given that: f(x)=cos3(4x-1)

Q: Construct an equation such that y = = C1e3z cos x + C2e3ª sin x is its general solution.

A: To determine the differential equation from the solution  Check the number of constant in the…

Q: COS X dx 1-sin x

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Q: b) Evaluate S e-2t sinht dt an

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