x2+1 =0 Has soluion in R

Q: Find the critical numbers of f(0) = 2 cos 0 + sin² 0.

A:

Q: dz 4. Compute where

A: We can solve the problem by residue method

Q: 2. Show that u(x, t) = cos(x – ct) is a solution of Ut + cuz = (0

A:

Q: 1 (b) Evaluate the integral S ; dx 2x2-12x+26

A: To evaluate: The integral of . Formula used: Integration Formula:

Q: x2 Vcos(t) +3 at 1. COS 2.

A: Given that, the integral ∫2x2cos t + 3 dt

Q: 8F OF OF 1. Use the formulas above to find and ду ax exy + sin (xyz) + In (yz) = 4 – z

A: Partially differentiate the function with respect to x.…

Q: 2x+8 c) Decompose 2x+8 dx. x(x+1)2 into its partial fractions. Hence, evaluate x(x+1)?

A:

Q: x*y"-xy'+y = 0 c) Y, = In x

A: Let's find.

Q: 11. Jlgull sin(2t +) dt %3D e2t-3 4 4. 64e3

A:

Q: 4 – dt 2 cos 4t 1.

A:

Q: cos(3rk) In k 5k k 1

A:

Q: 8 2 1. Reverse order, then integrate Sr) dydx.

A: Given:    Intergral is given

Q: 2. Use Method of Undetermined Coefficients: y" - 2y' + 5y = 4e*cos2x + n IN

A:

Q: find the general slühion with real values fn +y(H)=0

A: I am consedering y4(t) to be (y'(t))4

Q: Q3: Find the Wronskian for the following solutions. Y, = 1, Y =In

A: Wronskian= 112ln1+x1-xd1dxddx12ln1+x1-x= 112ln1+x1-x01x+11-x=1x+11-x

Q: 4. Find the Cauchy principal values of the following integral: dx. (x²+1)(x²+2x+2)

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Q: [0; 2n) v3 sen x+ COS X 16

A:

Q: Evaluate the integral. 1 cos 2t dt 2 7x/2

A: To evaluate the given integral.

Q: Evaluate the integral 3 2x cos(xy)dydx 2

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Q: 3. Use the IVT to prove that y = x ln x has at least one zero on 2'2

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Q: 10.) Find the integral of* 3 (-4y ) ( +14y-7) dy

A: We need to evaluate ∫3y6-4y-3y7+14y-2-76dy                          (1) Let y7+14y-2-7 = t On…

Q: (-1)"zən+1 (2n + 1)! sin = 3! (-1)"-2" (2n)! 21 1+r+ (-1)*+1," I+1) -E n-1 2! Pip- 1)(p – 2)a.. 3!

A: f(x)=f(0)+xf'(0)1!+x2f''(0)2!+x3f'''(0)3!+x4f'''(0)4!+ ⋯ +

Q: To prove that 2 dx 2 In V1 + (In x)² + In x| + C X/1+ (In x)² we use the substitutions

A: The given integral is ∫2 dxx1+lnx2 Find your answer below

Q: Compute dx using the techniques as presented in class and in our textbook. Show all 2x +5x-3 the…

A: we first factor the denominator

Q: Evaluate the integral. 3x-7 (a) S- dx x2-2x-8

A: Answer and explanation is given below..

Q: 4. Compute dx S in two ways and verify that the answers agree.

A:

Q: What is R2 if beta = 0?

A: Solution : Consider a linear regression model, Yi = α + βXi + εi It is known that, coefficient of…

Q: Expand xy² + 2x – 3y in powers of (x + 2) and (y – 1) upto third degree | terms.

A: Given ,  f(x,y) = xy2 + 2x - 3y  By Taylor's theorem  f(x,y) = f(a,b) + {(x-a)fx(a,b) +…

Q: 19. Find potential function for = (3xy, æ³)

A:

Q: y" + 3y' + 2y = cos4x %3D

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Find (1,0) where y2 + x2 + eV = 0

A: Given y2+x2+ey=0 ⇒y2+ey=-x2⇒ddx(y2+ey)=-ddx(x2)⇒2ydydx+eydydx=-2x⇒dydx(2y+ey)=-2x⇒dydx=-2x2y+ey

Q: 3. Prove that So 0 1 x + ex -dx = n=1 (−1)n−1(n − 1)! nn

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Q: Find all solutions of cos 2x V3 for x if 0 < x < 27. 2

A: on solving this we get the

Q: 2. If the Wronskian of y1 and y2 is e2" (x² + 5) and y1 = e2", find y2. %3D

A:

Q: Find a general solution of each reducible second-order differ- ential equation y" = (x + y')²

A:

Q: Find a general solution of each reducible second-order differ- ential equation y" = (y')2

A: Given, The differential equation y"=(y')2 .               ................(1)

Q: d 1 Prove that: dz (tan¬1 z) = 1+z?

A: Given query is to find the derivative of the expression.

Q: Calculate the residue of ez.z-5 at z=0

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Q: Solve the following DE using Separable method. 2y' = x(1- y')

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Q: 3t e"dt 2 (1+4e3

A: Let's integrate.

Q: 3 Find absolute extrema for fCx) = x°-9x´+15x -3 %3D in terval [o,3] Oへ

A:

Q: 1. y = Arctan 3-V9-x2 2. y = 4 Arccos + 2v4 - x2 2 y = In (*+2), (x-1)2 3. у%3DIn

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Q: prove using the IVT. e^x + ln x = 0 has a solution.

A:

Q: Find all solutiens of 62y -34x=8 with xry z0

A: Given: It is given that the equation is 62y-34x=8 with x, y≥0. To find: All the solution of the…

Q: Solve the diffesential equation 2ber 十X

A:

Q: Find the general solution of the following first-order ODE xy' = y + 2x' sin² (2)

A:

Q: 3: Solve ODE Cist Order a. dY

A:

Q: y = In[(2x – 1)(x + 3)] with Respect to x by using the chain rule.

A:

Polynomials

Try substituting 1. You will get 6 and not 0. Try other real values also. What About -2? Let us check.