(b) Show that o = 2[Rx(0) - Rxx(0)] XX

Q: 13.Show that the third-order Adams-Moulton formula is yn+1=yn+h12(5fn+1+8fn−fn−1).

A:

Q: Find the general solution to the yiven Euler x* j -3xy = 2.

A: Given differential equation is x^2y" - 3xy' + 9y = 0

Q: 0, 0<x<1/n, fn(x) = { /n, 1/n < x < 2/n, 2/n < x<1. 0,

A: Pointwise convergent:- A sequence of function is pointwise convergent, if its every point sequence…

Q: - Find the antiderivative, FCx), and Check your answer of the funetionçiven xZ+3x+5 by f (x)=

A:

Q: Find for x³+y³ = 2. -4x O O (E) None of these ○ 3x² + 3y² = 0 2x *(*_*) O

A: Note:- As per the company guidelines we can solve first question. I hope that the given solution…

Q: Show that x +2 and oe) = *+6

A:

Q: 13-30 Evaluate the integrals using Part 1 of the Fundamental Theorem of Calculus. 4. L_ Ax 4x(1-x²)…

A:

Q: 5) Solve xy' + y[1 – In(xy)] = 0 by using a suitable substitution in terms of x and y.

A:

Q: Derive a formula for In x dx where a. nt-1 b. n=-1

A:

Q: The integral of the given function ∫csc^6(x) dx is equal to

A: Need to find ∫cosec6(x) dx

Q: 1. Find for y = In () (A)+ 1 3x-2 X-1 1 x-1-x2 (B) x2 - -- x-1 x (х-1) x2 x2(x-1) x-1 1 X-2 (D) (E )…

A:

Q: 2. (xD-2)(D+4x)

A: We have to perform the multiplication on the differential operators (xD-2)(D+4x) .

Q: x2n+1 El-1)"; 2n +1 n=0

A:

Q: let y = 3 x2 + In x - ex find y' O 6x + (1/x) + ex O 6x-(1/x) - eX O 6x +1 + ex O none of the above

A:

Q: 8 4 8 Suppose that f(x) dx = 7 and f(x) dx = -6, and g(x) dx = -1 and g(x) dx = 4. Compute the given…

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

Q: Solve the ODE: xy"+2y'-xy Oby using the Frobenius method.

A: Given that ODE: xy''+2y'-xy=0                    .....1 We know that the solution to this ODE is:…

Q: Ym - 21 , prove that + (n? m² ) yn =o 2 + (2n+1)x Ynts

A: Given y1/m+y-1/m=2x To prove that  x2-1yn+2+2n+1xyn+1+n2-m2yn=0 Solution :  y1/m+y-1/m=2x…

Q: Find the general solution to the Bernoulli-type ODE x²y' + 2xy = y°, for x > 0.

A: Bernoulli's equation is a special type of first-order linear ordinary differential equation. When…

Q: B// findZ transform | x(n) = (0.8)" u(-n- 1)

A: Solution

Q: What is the coefficient of x^n for the generating function (1)/(1+x)^2?

A:

Q: 9. The value of ¹₁ O True False [Tn (x)]² dx = 0, for each Chebyshev polynomial T₁(x), n > 0.

A:

Q: 10. Find the integral of dx x²-4 O In() + C x-2 O In() + C 2x x+2 O fIn( *2) + C X+2 O In() + C x+2…

A: *using concept:- 1. Partial fraction. 2. int(dx/x) = ln(x). 3. ln(m) - ln(n) = ln(m/n).

Q: хах 11. The integral f 4-х2 is equal to 1 A. In | | + C C.-글m14- x리 + C 4 x+2 2+x B. In |4 – x2|+C…

A:

Q: Show that r n2n-1 r=0

A: Want to  prove:    ∑r=0n rnr=n2n-1

Q: the Fundamental Theorem of Ca -5 (x³ – 9x)dx. v3

A: Here we have to use fundamental theorem of calculus to find the exact value of  ∫05(x3-9x)dx…

Q: Show that the generating function for compositions into an even number of parts, each of which is…

A:

Q: Evaluate / xdx x2+6x+13 Select one: 글 In (x2 + 6x + 13)-Arctan꽉 +C In (x? + 6x + 13) – Arctan O a.…

A:

Q: 12. Find the general solution using Reduction of Order: a) y"= 2ln x b) y" + y' = cos 3x

A: We have to find the general solution: y''=2lnx. Here, the value of y1 is not given.

Q: 4. Prove that if f(x) = agx" + a,x"-1 +..+ an-1x = 0 has a positive root x = xo, then the equation…

A: Note that f0=0 and that fx0=0. So using mean value theorem there must be some 0&lt;λ&lt;x0:…

Q: 6. What is the coefficient of x'y" in the expansion (4x + 5y) s. Show your work here:

A: We find coefficient of x7y8 in the expansion (4x+5y)15

Q: and X4 %3D If the engine type is traditional, then x3 = When you plug in these two values in the…

A: When the qualitative predictor has m levels then we create (m-1) dummy variables. Here the…

Q: 12. Find the general solution using Reduction of Order: a) y" = 31n x

A:

Q: 9-x2 B: Find the integral S 18-x2-y xydzdydx.

A: We have to calculate the given intregration

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: 2 In x 1 e* 2 1 In 2x -1

A:

Q: 12. Find the general solution using Reduction of Order: a) y" = In x

A: you have asked multiple questions in a single request we would be answering only the first question…

Q: 1 3 3. Use the IVT to prove that y = x ln x has at least one zero on 2' 2

A:

Q: Simplification of In x + In(x + 1) = 0 is Ox2 + x-1= 0; x > 0 Ox2 +x +1%= 0; x > 0 %3D x2 +x-e = 0;…

A: Given: ln(x)+ln(x+1)=0

Q: Example 19-36. If U, = a + bx+cx², prove that 3 U, dx = 2U2 + 12 (Uo- 2U2 + U4) 1 and hence find an…

A:

Q: 2 1. Evaluate the integral: dx 2 x2-x

A:

Q: Evaluate O |x + 1/² |x - 21³ O 3 ln x²-x2 + C In In In O In x+7 x²-x-2 ·S B +C |x+2/8/3 |x-1|5/3 |x…

A: This question can be solved using the concept of partial fraction.

Q: In x + In(x – 1) = 10 In(x + 25) – In(x – 1) = 3 e2x – 2ex = 15 e2x – ex – 12 = Q %3D %3D -

A: i) ln x+ln(x-1)=10ii) ln(x+25)-ln(x-1)=3iii) e2x-2ex=15 Note:      Multiple part question are given,…

Q: 8. Find a recursion formula for the family of integrals I (n) = r I(1 x" sin x dx that starts with…

A: Given a family of integrals, I(n)=∫xnsinx dx

Q: 19. Consider the integral f√x²+25 dx. 9x² a. In/√x² + 25 +x/- - b. x+ In/√x² + 25/+ √x²+25 9x √x²+25…

A: Solve the integral  √(x2+25)/9x2

Q: e-1 : Compute Lt 1+x-1,

A:

Q: Find the torolrootsS 1.X +2=0 2x-3x+ム=O 3.X22=D0 4.(X-3)=-ム 5.(x+1)を 6.-3x+19X-2ム=O 7.Xー3=1 8.1.5X=6…

A: According to the guidelines issued by the company we are supposed to answer only first three sub…

Q: In ( x² + 3x -=-7) dx X-2 Evaluate the integral: Se Ⓒ + A x² 2 =+ + In|3x-6|+C ℗ +² +5x+3n|x-2/+C B…

A: To find out the integration.