Prove thiat dx Ś (areten()) ) = し 4+X

Q: Find the implicit deriviate (dy/dx) of (2x+3y)1/3=x2

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Q: Use Green s theorem to evaluate the give (y² dx + 8xy? dy)

A: In this question we will use basic of calculus i.e concept of integration. We will use green's…

Q: In(x) 1. Evaluate -dx if possible. If not possible, explain why.

A: As we know that the integration by parts:- ∫udv=uv-∫vdu

Q: tan zeecz coS z

A: Integration is the process of finding the anti-derivative function of the given function.…

Q: 4. Evaluate the integral. S tan (2x) sec°(2x) dx

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Q: 1+cscx cotx integralf dx is ec X-CSCX

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Q: Prove that Va2 + 4 sin ( sec %3D V2 +4

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

Q: 2. dx Ix Also, Prove that 22 %3D dxdj = dy dX

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Q: How would you choose u when evaluating x" cos ax dx using inteeration by parts?

A: Given integral is ∫xn cos ax dx

Q: Directon. tanx 6. Oy= (sinx) Fan a ANS: AN

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Q: 2. Show that P(1-x)° dx= x'(1-x) dx. %3D 0/

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Q: Obtain a-(In x)? dx.

A: Given,  ∫x-5(lnx)2dx

Q: y = sin(x + y)

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Q: it Z = exY , where : x= Incutv) and y = tan () %3D find a) du శ్రీశర శశ్ర

A: Given,  z=exy ; where x=lnu+v and y=tanuv To find: partial derivatives

Q: Prove: cosh 3x = 4cosh'x- 3 cosh x %3D

A: We will solve the following.

Q: : )-+(÷), zw= (C) dx 1 et %3D dt 1 (: :)-+(-), -= (C) dx dt 1

A: Given dxdt=0110 x +ete-t Here let take A= 0110A-λI=-λ11-λ=0λ2-1=0λ=±1 Hence the eigen vector for 1…

Q: use the Mean value Theorem to establish Isine-siny </2-y) Ve,yER

A: We will prove the inequality as following.

Q: Prove Sinhu.sinhv=1/2 (cosh (u+v)-cosh (u-v))

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Q: Find dy of Using first principles

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Q: r(10,3,3) dx (1,1,1) dy dz. - -

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Q: Find dy ду é^sinx in sx

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Q: What do you mean by euler's theorem?

A: Euler’s Theorem is a generalization of Fermat’s little theorem dealing with powers of integers…

Q: Evaluate f, f,(1-2) L(-dy dx dz

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Q: tan °(ln z) sec® (In z) Evaluate dz.

A: Evaluate: ∫tan3lnxsec6lnxxdx

Q: 6. S sin (3x – 1) dx. cos Vi dx. 7. Evaluate th dx. Show yo 8. 3 dx. S (! + 1)(t – 1) dt. 9.

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Q: Explain why the fundin f(2)= 526+ z COSZ - z’e? is entire ?

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Q: Evaluate 2Sin x´dx, by (i) mid-point rule, and (ii) Simpson's 1/3 rule.

A: i)Given:        ∫242sinx2dx   Mid-point rule:       ∫abf(x)dx=∆xfx0+x12+fx1+x22+fx2+x32+...…

Q: Prove that d /dx ( cot -1 x) = - 1/ ( 1+ x 2 )

A: we have to prove that: ddx(cot-1x)=-11+x2

Q: If X; derive the moment-generating function (mgf) of X?. Ν (μ, σ) :

A: Given X~ N(mu, sigma^2) We want to find the mgf of X^2

Q: d - In(u²) dt dx et

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Q: Evaluate | sin'x +cos°x dx Select one: 6*4*2 5*3*1 7*5*3 6*4*2 6*4*2 5*3*1, TT 7*5*3 6*4*2 2 O None…

A: By the using the formula we will solve the above integral. If n is an integer ≥2, then…

Q: Compute ∫xsin(3x−2)dx.

A: Let the given

Q: 11 Show that dy dx = 1-In2. 8(xy +1) 0 0

A: Follow next step

Q: compute (x2 - 8x +20) dx on the interval (0,1)

A: To evaluate the given definite integral over the open interval (0,1)

Q: Find dy ify Yify = sın 2x. dx

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Q: Limit _π/2 toπ/2 integral (1+cosx) dx

A: To integrate: ∫-π2π21+cosxdx Solution: Property of definite integral states that: ∫-aafxdx=2∫0afxif…

Q: 4. You will need to use L'Hopitals Rule in this one Sxe-* dx

A: This is a improper integral problem

Q: 16 Iny dy

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Q: Fn C) = show sin nx ス|L Sinnx

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Q: Ssin(x)cos(2x)sin(3x) dx sin(3x)cos(3x), sin(2x)cos(2x) , sin(2x) + + C 12 8 8. 4 sin(6x) sin(2 x),…

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Q: This is exercise 26 of Section 7.5 page 460. Find the integral æ* sin(æ²) dx-

A: Answer is given in the picture

Q: dy+チ=-

A: Note: Since you  have mentioned multiple question, I answered first problem. If you need answer of…

Q: What is the number of derangements D4 of the set {1, 2, 3, 4}? (Give the exact

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Q: Compute dx in two ways and verify that the answers agree.

A: Assume the given integral be I. I can be integrated via trigonometric substitution by substituting…

Q: Sin'z dz 4.

A: Note :- These are multiple questions and you not mention here whose solution you want. So i am…

Q: er dy %3D sec da

A: The given differential equation is exdydx=sec y and the initial condition is y0=1. Solve the given…

Q: EA H.w : Does. fcz)= Continuous at cis

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Q: dt 4e -et

A: To evaluate the integral: ∫dt4e-t-et Solution: Given integral can be written as:…

Q: 6. y 45

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.