b) Prove the second De Morgan law in by showing that if A and B are sets, then AUB=ANB i) by showing each side is a subset of the other side. ii) by using a membership table.

Q: 7. In the differential equation 4(3x+ y-2)dx-(3x+ y)dy=0, we let the substitution dw =- (Note: We…

A: Given differential equation is 4(3x + y - 2)dx - (3x + y)dy = 0

Q: Find the solution. (x+e) dy - dx =0 (A y=ce" + ye B x=ce" + ye" x=ce + ye D y=ce" +xe

A:

Q: Determine the general equation of the plane containing the points P(1, -4, -5), 3 Q(2,0, 13) andR

A: We have to determined the general solution of the plane that containing the points P(1, -4, -5),…

Q: 2. Prove the following recurrence relation is satisfied by the given closed form using strong…

A:

Q: Show that The Hermite polynomials can be difined by the integral representation H, (x) = (-i)"2"e**…

A:

Q: Find the solution. dy 2y = 2r/y dx A y = x³(x+c) 3 B y = x(x+c) © y = x²(x+c) 2 Dy = x²(x-c) -2

A:

Q: Q6. Use the method of Variation of parameters to solve (i) y" + y = tan x. (ii) x²u"+xy' +(x² – !)u…

A:

Q: Solve the system of inear equations, using the Gauss-Jordan eliination method. (Ir there is no…

A: We have to solve the given system.

Q: Match the following definitions to the correct terms.

A: # as per the guidelines we are entitled to solve three subparts at a time, please resubmit the other…

Q: A. Find the area enclosed by each of the following curves. T= 4 sin e

A:

Q: You want to receive ​$400 at the end of every six months for 5 years. Interest is 11.8% compounded…

A:

Q: Approximate the roots of the polynomial f(x) = X³ - 7X + 6 using False-position method. %3D

A:

Q: Evaluate the double integral. dA, D x² + 1 D = {(x, y) | 0< x< 7,0 < y < Vx}

A:

Q: Find the solution. (D* + 1802 + 81)y = 0 Ay = (c, + c,)cosår + (cz+c,)sin3r. ® y = (c, + cx)cos3r +…

A:

Q: Ikeoluwa collected data on whether 65 professional golfers have practiced for at least 10,000 hours…

A: A Venn diagram can be represented as diagram representing mathematical or logical sets pictorially…

Q: a Write down the derivative of arcsinx. b Use integration by parts to find | arcsinx d.x.

A: a. Derivative of arcsin(x) is given by ddx(arcsin(x)) = ddx(sin-1(x)) = 11 - x2

Q: Use the Gauss-Seidel method to find approximate solutions to -21 + 3x2 + 23 = 5 2x1 + 2x2 + 5x3 1…

A:

Q: 4. Substitution Suggested by the Equation: (x+2y-1)dx+3(x+2y)dy=0

A:

Q: 3. Determination of integrating factors: 2y(x+ y+ 2)dx + (y -x -4x-1y = 0

A:

Q: 2. The linear differential equation x*dy+(2y-3x²y-x' dx 0 has the integrating factor equal to (Note:…

A:

Q: Find the solution. y-y = -xyl/2 y =(x+2+ce½,? B y = (x+2-ce/½,? © y = (3r - 2+ ce/½,? = (3x –…

A: The given differential equation is ,       y' - y =  - x y(1/2)  Bernoulli equations :  An equation…

Q: -x2 +y ar 49 xy plane: y? x 25 y? plane: y? as 49 2.

A: To sketch the graph of: -x29+y225-z249=1.

Q: 7. Express the solution of y" + 2y' + 2y = sin (3t) convolution integral (you don't need to evaluate…

A:

Q: When the centered difference approach of f (x) = sin r - a+1 is used to estimate the first…

A: When the centered difference approach of f(x) = sinx-x³+1 is used to estimate the first derivative…

Q: 4. Let F(n) = 2F(n – 1) + 5F(n – 2) – 6F(n – 3) with initial conditions F(0) = 4, F(1) = –4 and F(2)…

A:

Q: Solve the system of first-order linear differential equations. (Use C1 and C2 as constants.) Yı' =…

A:

Q: [2 - 3 2 - 3 and be express as A = LU as below L4 – 1 - 2 1 c) Let A = |1 | 01 [u11 U12 U13 [2 - 3 2…

A:

Q: Let matrix A = 1 1 1 3 2 1 −2 3 1 (a)Find two distinct row echelon forms of A. (b) Find the…

A:

Q: Without using the membership table approach, prove the identity (AUB)nC=(AnC)U(BnC)

A:

Q: For x, y, z, w > 0, prove that (x/z)+(y/z)+(z/w)+(w/x)≥4

A: It should by x/y, instead of x/z

Q: Using the Divergence Theorem, evaluate I= F-ds where S is the sphere of radius 2 centered at the…

A:

Q: if j = 1     the expression is x if j = 2     the expression is kx + x if j = 3     the expression…

A: if j = 1     the expression is x if j = 2     the expression is kx + x if j = 3     the expression…

Q: 1 Find the Inverse Laplace Transform of s2+2s+ 10 (A -e "cos3t 3 1 B -e -'sin9t 3 3r -e"cost D -e…

A:

Q: 2. Use zero- through fourth-order Taylor series expansions to predict f(2.5) for f(x) = ln x using a…

A:

Q: [2 - 3 2 – 3 and be express as A = LU as below L4 1 c) Let A = 1 1 2 [2 3 1 1 [U11 U12 U13 - 7 l21 1…

A:

Q: Find the laplace of each f(t) 5. 2t'e 4t

A: Solution

Q: cos(r+1) In(z-1) Simpson's % rule. with four segments. Evaluate f (x) = from to using 5m 13 %3D…

A: Mathematical methods used to solve equations or evaluate integrals or solve differential equations…

Q: Give the parametric and symmetric equations of the line that passes through the point (4, -3,5) and…

A: The given point is 4,-3,5. The given vectors are 2,6,1 &amp; 1,3,-5. The equation of plane having…

Q: Determine if the vectors are linearly independent Justify your answer. 6. 12 - 36 The vector…

A: The given vectors are                                     700,    8   3-6,    9  12-36 We have to…

Q: Tests for Convergence 1. Consider the series Inn n=1 a. Use Comparison test to show that the series…

A:

Q: A particular specie of animal has a carrying capacity of K and a growth rate of r. From an initial…

A:

Q: 31. Let R* have the Euclidean inner product. Use the Gram- Schmidt process to transform the basis…

A:

Q: For the following relation ~ on set X, determine whether it is symmetric, transitive or reflexive.…

A: For all x in X, x2 ≠ x2 + 1,hence x ~ x Hence ~ is reflexive.  Now consider the equation          x2…

Q: Solve the given partial differential equation a² z %3D dx? at?

A:

Q: Solve the system of inear equations, using the Gauss-Jordan elimina the parametert. Use s if a…

A: According to our guideline we are supposed to asnwer only first asked question.kindly repost other…

Q: dy = 0 ? What is the general solution to the differential equation y dx² dx

A:

Q: Solve the given system of linear equations using the Elimination Method. 4.)     2x1 + 7x2 + 15x3 =…

A:

Q: What is the particular solution to the differential equation x + (1 + x)y = 12 with y = 0 and 2 - 0…

A: The solution is given as

Q: Since an instant replay system for tennis was introduced at a major tournament, men challenged 1413…

A: Q = 1 - P = 0.7063 Test Statistic is given by:Z = (0.2951 -0.291)/0.0205 = 0.20 So, Z = 0.20

Q: Evaluate the integral shown using Simpson's 3/8 Rule with 30 panels. 12 ) dx 4arctan O 32.52059525…

A: Given integral is ∫2124arctanx6dx