6. Setting æ = cos 0 show that T.(e) = [(- + ivI- =')" + (* - ivī- =')"] n where i = V=1.

Q: The graph of g(1) is shown below. The areas trapped between the curve and the I – axis are labeled…

A: The solution is given below

Q: 3. Let R be the region below bounded by the parabola y = 4 – x2 and the lines 3x – 2y + 3 = 0 and y…

A: The given curves are y=4-x2, line: 3x-2y+3=0 and y=0. To find: (a) definite integral such that it…

Q: Hiws slove du dt 4 dx2 K= 8. h=1 u(o,t) =0 u (8,+)=c U(x, a) =0 = 4 X- (5)X |

A:

Q: (b) Let F be the set of functions of the form f(x) = A sin(x) + B cos(2x), where A, B are some real…

A:

Q: 11. Let R and R' be two rings. A mapping f: R→R' is called an antihomomorphism, if f (x +y) =f (x)…

A: Let x, y ∈ R. Then (g)(x + y) = f(g(x + y)) = f(g(x) + g(y)) = f(g(x)) + f(g(y)) =(fg)(x)+(fg)(y),…

Q: Suppose n is an integer. Prove by direct method: If n is an odd integer then 8|(n² -1).

A: suppose n is an integer.  prove by direct method - if n is an odd integer then 8n2-1

Q: (-0.1)-(30)+ (-0.1)' (150) f(-0.1)%= 2 (-0.1) 3(-0.1),11-0.1)- (120)= 6.83 9. 4.

A: f'(-0.1)=111+-0.1-123(30)+-0.122--0.1+13150+-0.136-3-0.124+1112-0.1-14120=6.83 (a-b)3 = a3-3ab(a-b)…

Q: Find the laplace transform of the following: a.) f(t) = teatcosbt b.) f(t) = 7t + 6et - 2et - 10…

A:

Q: If matrix multiplied by s equal to zero, then matrix C-4 D o

A:

Q: construct a cayley table for the dihedral group of order 5

A:

Q: - Using the Maclaurin Series for e (e* = E=o) a. What is the Taylor Polynomial T3(x) for e centered…

A:

Q: Find the Laplace transform of 1. f(t) = [1 – Uzn(t)](2 sin t – sin 2t) t², 0 2

A:

Q: (a) y = x +2 and y = x. (b) y = cos x, y= eª and x = .2 .2 ElN

A:

Q: prove it .The set of all optimum solution of the general convex programming problem is a convex

A: Proof

Q: 5 solve the 1UP: y% 4y(2)+ 3y'= Y1)=e+ % ,uG) = et %

A:

Q: 5. A sequence of elementary row operations was applied to a matrix A to put it in an upper…

A:

Q: (b) Unitarily diagonalize the following matrix 3 -6i 6i 6 -

A: We have to diagonalize the given matrix A=3-6i6i-6 unitarily

Q: Determine the exact solution of the following differential equation y = 2 - y at y(0) =1 So the…

A:

Q: 04) Find the largest eigen value for the matrix 1 2 A= with x" (0) =(7/17 1) T. 5 4

A:

Q: Using the method of variation of parameters, what is the form of a particular solution y of (D³–…

A:

Q: Hiws slove du 4 dt %3D dx2 u(6,t) = L (8,t)=0 U(x, a) =0 : =4X-()x²

A:

Q: Solve the DE: dy + 2xy = 2x³y3. dx

A: The given problem is to solve the given differential equation. The given differential equation is of…

Q: A particle is moving along the path given by R(t) = (sin(ln t), cos(ln t), v/3 In t). (a)…

A: We need to find arc length of given curve to do arc length parameterization  arc length of curve…

Q: PROBLEM NUMBER 1 A farmer can plant up to 8 acres of land with wheat and barley. He can earn $5,000…

A: We will use basic knowledge of linear programming to answer this question correctly and completely.

Q: 4) Solve the boundary value problem y -3y' + 2y = 0 with y'(1) = 1 , y(3) = 2e* - e? h = 0.5

A:

Q: 1. (D² + 4)y = 4cos' x

A:

Q: Evaluate the Inverse Laplace Transform: 4s-2 F(s) = s2 –6s+18 O f(t) = 4e* (cos 3t – sin 3t) - O…

A:

Q: Compute forward difference approximations for the first derivative of the function, y = e*cos(x²),…

A:

Q: Q5) Solve the equation with y (0,1) = y (1,1) = 0 y (x,0) = sin x ! = 0,0 sxSI 8. ду (х .0) and…

A:

Q: SOLVE FOR INVERSE LAPLACE TRANSFORM 6s – 4 - s2 4s + 20

A:

Q: In a series of ten tosses of two distinguishable dice A and B, the following faces are uppermost…

A:

Q: Compute backward difference approximations for the first derivative of the function, y = log(x² +…

A: We have to compute backward difference approximations for the first derivative of the function,…

Q: If 1 <p< o then P is separable.

A:

Q: QUESTION 1 Find an integer x between 220 and 260 that satisfies x = 39^123 (mod 41). Your answer…

A: We need to find integer x between 220 and 260 that satisfies x = 39123 mod 41 Clearly , 39 and 41…

Q: Use the Gauss-Seidel iterative technique to find the 3rd approximate solutions to 2x1 + x2 – 2x3 = 1…

A: we take x1=w, x2=y, x3=z So we need to solve the system  2w+y-2z=12w-3y+z=0w-y+2z=2 Starting with…

Q: Since question b has 5 parts to it its still 1 question

A: Given that,y=48×0.99twherey is temperature of liquid in degrees celsiust is time in minutes. The…

Q: o) Let v1, v2, V3 be three vectors in F and let W = span {v1, v2, V3}. O What is the largest…

A: Given that v1,v2,v3 be three vectors in F114 and let W=spanv1,v2,v3. (a). Since v1,v2,v3 are three…

Q: 8 Given a function: f(x) (х-7)(х-1) Write down the definition that lim f(x) = L = 1| 8 oProve that…

A:

Q: -x-x² + = X-. to 2 decimal place accuracy 8. Determine the range of x-values for which e*

A: Given: xex=x-x2+x32 To find: Range of x values

Q: In n n + 1 а) аn b) an = n n 1+ (-1)" c) An 1 d)an n II

A: Note:  Since we can solve at most three subparts in a question, we have solved the first three…

Q: -3 -1 Let A = ( ), and B = ( ) C = 2A - B What C1? a = %3D C = %3D 10

A:

Q: I. Change the following number systems to base- 10 numbers. (Show your solution 3 X 5 points) 1.…

A: Please find the answer in next step

Q: Q3) Solve the following boundary value problem using finite difference method dy +2y = 0 dx y(3)=…

A:

Q: (c) Use fzero to find when the derivative of 5. S(x) = 9. cos(x) sin(x) is 0 in the interval (0,…

A: NOTE: As per the guidelines we are supposed to answer only one question because all parts or…

Q: Let G, (Isisn) be n groups and G is the external direct product of these groups. Let e, be the…

A:

Q: III. In a particular very small region, the consumer price index, C, depends on the current valuc of…

A: Given information C = 100 + e-EPF where, C = Consumer Price Index E = Gross Domestic Regional…

Q: Prove the statements: Use mathematical induction to show that E, ar*-1 a(1-r") for all integers n >…

A: Show that ∑k=1nark-1=a1-rn1-r for all integers n≥1, where r≠1. Prove the equation is true for n=1.…

Q: (b) Perform the Gram-Schmidt orthogonalization process for u = x +1, u2 = x² + 3, u3 = Va using the…

A:

Q: (a) Determine the Inverse Laplace transform of the following expressions: 1 (s-4) (b) The linear…

A:

Q: Find an approximation of v2 using a bisection method with the following steps. (a) Set up a function…

A: