Evaluate the integral 3x+2 dx by interpreting it in terms of areas. Draw the graph and shade the area.

Q: Ex. 2. Find a reduction formula for e" sinm x d, where m>2 %3D In the form (1+m") Im=m(m-1) Im-2 %3D

A: Using the integration by parts

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Q: Connider the Legendre's litterential equation Cl-x²) Y" - 2xy Any soluhion tuis" equation is…

A: Solve Legendre differential equation by series solution.

Q: 2. Let A = Find 3A +2 3A+2B = %3D

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Q: Solve the initial value problems.

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A: The solution is given in the next steps.

Q: ORTHOGONALITY OF BESSEL FUNCTIONS x J, (ax) J, (Br) dx = 0 where a and B are the roots of Jn (x) =…

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Q: Find the Fourier series of the function -1 for - π<χ < | f (x) = for < x < - TC + 1 for < x < T.

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Q: (-1)"n+1 if \피 <1. Given: In(1+x) = %3D n+1 Find the Maclaurin series for ƒ(x) = x In (1 + §).

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Q: 19. Given differential equation, which of the following is true. a) y, and yz are fundamental set of…

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Q: Given: A = 0.6 – j0.4 B = 0.5+ j0.8 C = 0.6 – j0.8 D = 0.5 + j0.4 %3D Evaluate: (C+B)/ log.…

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Q: 1. Get examples of: o a theorem with a direct proof, and o a theorem with an indirect proof. The…

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Q: Exercise 25.2. Prove that log, (bc) = log, b+ log, c (mod p- 1) for all b, c not divisible by p.

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Q: Question 10 : Find all values of k for which A is diago- nalizable, given that A =

A: Here i include both real and complex cases

Q: Q.1 Find local extrema and saddle points, if there are any. f(x, y) : 3 y3 3 x² – 4y - - 3 2

A: It is given that fx,  y=x33+y33-32x2-4y. We have to find the local maximum, local minimum and the…

Q: Evaluate the integral (C (-2)sin(x² + y² ) dydx . Sketch the region R in the xy-plane. Jo

A: Evaluation of the double integral, by using conversion of polar coordinates

Q: Let K be a field. Consider the following set {(::)- a1 0 R:= a2 a1 (a) Show that (R, +) with the…

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Q: Jacob has $4,800 to invest in a saving account. He receives a steady interest rate of 3.35%…

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Q: cide whether the following statement makes sense (or ia clearty true) or does not make sense (or in…

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Q: Verify the trigonometric identity sin(z - 1/2) = - cos(z)

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Q: Find the interval of convergence of Σ (-6)" (х + 10)" п! n=0 (Use symbolic notation and fractions…

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Q: Show that 1.3.5... (2 n – 1) (i) P2n (0) = (– 1)" (ii) P2n+1 (0) = 0. 2.4.6 ... 2 n

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Q: Find the extrema of the function below 10 - (x-5)²- (y+3)²

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Q: find the fourier series for the half-Periof sine of the function fxj = sinx inthe period x Then find…

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Q: onsider the following IVP: y'' -3y' -10y = 1, y(0) = -1, y'(0) = 2

A: Given differential equation is y'' - 3y' - 10y = 1 ; y(0) = -1, y'(0) = 2

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A: For the solution of the problem follow the next step.

Q: 23. For the differential equation y"+y = 3 sin(2t) +t cos(2t) the form of the particular solution is…

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Q: Find the Laurent series expansion of each of the following functions in the indicated annulus. (a)…

A: (a) fz=z4sin1z where 0&lt;z&lt;∞ It is known that sin z=z-z33!+z55!-.... Then…

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Q: 3. What we want to do next is write (x + jy)as Reie where R= J(x? + y? ) and tan-(e) = (2)

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Q: Find the Laplace Transform of e-2* cos3t + 5e-2t sin3t (s+2) + 15 A) (s2+4s) + 13 15 + s2+9 В s2+9…

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Q: The graph above shows the polar curve 7 = 28 + cos 8 for 0< e < a. What is the area of the region…

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Q: Find the Laplace transform of f(t) = (t² + 1)²

A: Use Laplace table.

Q: 8. consider the differential equation x*y3 + x(1 + y²) = 0 Which of the following integration factor…

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Q: 3. Let F(n) = 9F(n – 1) – 24F(n – 2) + 20F(n – 3) with initial conditions F(0) = 1, F(1) = 5 and…

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Q: tices of ΔA'B'C produced by T−3, 6 (ΔABC) = ΔA'B'C?   A. A′(0, 6), B′(0, 4), C′

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