2.let and B be sets.  Prove A ∪ B = A∩B if a = b

Q: 2. Find the volume of the solid under the surface z = = 5xy and above the region in the. xy- plane…

A: Volume bound by the xy-plane

Q: Q2: Solve the given differential equation. a- Analyze the DE and visualize the solution (write the…

A:

Q: Let R be the region bounded by the graphs of C₁ = ( x − 3 ) ² + X (0, 0) 9 + y² = ₁² and C₂: y =…

A:

Q: Which of the following statements is correct about the set -3 6 -898) 2 -4 -2 S = Select one: O O O…

A: There is set S given. One has to check whether S spans the vector 333 and vector space R3 or not.…

Q: 8. u(x) = 2 aj's -1 8 cos xtu (tj dt

A:

Q: a. Find the linear approximating polynomial for the following function centered at the given point…

A:

Q: . Verify Stoke's Theorem for F (x, y, z) = (3y, 4z, −62) and S is the part of the paraboloid z = 9x²…

A: Given That : F→=3yi^+4zj^-6zk^ and S is the part of the paraboloid z=9-x2-y2that lies above the…

Q: 6. Complex trigonometric functions, ODE and independence 3π a) Find the real part of following…

A:

Q: Find the Inverse Laplace Transform. 14s² +70s +134 (2s +1)(s² + 6s +13)

A: Find the Inverse Laplace transformation

Q: Let W be the set of all 2 x 2 matrices [a b]. d basis for W is S = (a) following questions: (b) • y=…

A: Given that W be the set of all 2×2 such that W=abcd|c=0 and d=2a-3b. We have to find the basis for W…

Q: Problem 6. Suppose S is an invertible 3 by 3 matrix. Consider all matrices A that are diagonalized…

A:

Q: a) Find the real and imaginary parts of cosh y+i

A: Since both are different so as per our guideline, we are supposed to solve only first question.…

Q: Let W be the set of all polynomials of the form a3t³ + a₂t² + a₁t+ ao where a2 = 0 and ao = 1. Then:…

A: Given: W is a set of polynomials of the form a3t3+a2t2+a1t+a0 where a2=0 and a0=1. And the given…

Q: A plane is heading 34 degrees west of south, after 240 miles the pilot decides to change the…

A:

Q: (i) = 5. If r(t) = tcostī + tsintī+3tk, Answer each of the following: Find an equation of the…

A:

Q: A bank features a savings account that has an annual percentage rate of r = 4.5% with interest…

A: Compound interest formula is given.

Q: b) Use Green's theorem to evaluate SF o dr where F(x,y) = (ycosx - xysinx, xy + xcosx) C and C is…

A: Green's theorem

Q: 4) Solve Poisson problem for a=lı b=l ↑u (x₁b) = f₂(x) ty b (0₁4)=9₁(y) 0 Ou=f(x,y) u(a.y) = 9₂ (9)…

A: Use separation of variables for laplace problem then from there go to poisson problem

Q: Find the particular (non-homogeneous) solution to the equation: d²y dx² - 3 dy dx + 2y = 4x²5

A:

Q: -8 X (x²+4)³/² -dx (use proper notation)

A: Given: ∫-∞∞xx2+432dx We have to evaluate the given integral.

Q: Find the arc length of the curve on the interval [0, 2π]. Hypocycloid perimeter: x = a (cos(0))³, y…

A: The given problem is to find the length of arc that is the perimeter of the hypocycloid within the…

Q: 12. Test each series for convergence or divergence. State the test used. (a) i Inn 8n n=1 (b) (-1)"…

A:

Q: Consider the following parametric equations. a. Eliminate the parameter to obtain an equation in x…

A: We eliminate the parameters.

Q: The cost of a book has been reduced from $3.00 to $2.55. Find the percentage reduction.

A: Given that The cost of a book has been reduced from $3.00 to $2.55.

Q: If α is an upper bound for S and α ∈S, then α = lub S.

A:

Q: Write the following series in sigma notation. Then find the value of the series or, es diverges,…

A: Given series is 20-12+365-10825+...

Q: There are two machines available for cutting corks intended for use in wine bottles. The first…

A:

Q: 1. Show that Led edx + (xe" + sinz)dy + ycoszdz is independent of the path and evaluate the integral…

A:

Q: Find the first four nonzero terms in the Maclaurin series for the function. f(x) = sin x cos x…

A: The given problem is to find the maclaurin series of the given function upto first four non zero…

Q: Consider F and C defined below. F(x,y,z)=xy i+ (1/3)x³j+xy k C is the curve of Intersection of the…

A:

Q: Given the following preference table, the Condorcet winner is OR S OT RANKING 15 12 1st 2nd 3rd 4th…

A:

Q: F(t) = (sint — tcost)ī + (cost + tsint)j + 2t²k, answer each of the following: Show that the curve…

A: Given: rt=sint-t costi+cost+t sintj +2t2k To find:  (iii) The curvature of the curve as a function…

Q: Calculate the iterated integral. Г.Г Jo 1 5 √s + t ds dt

A: Evaluation of the double integral

Q: a) Solve y" -6y' +9y=0. b) Find the particular solution of y"-6y' +9y=3-t c) Use the Laplace…

A: THE SOLUTION IS GIVEN BE

Q: Find the Taylor polynomial at x = 0. If f(x) = ln(1 − x²).

A:

Q: 2) Given the following polynomial: f(x) = x³ - 2x² - 5x + 6 a) Determine the end behavior in proper…

A: This is a multi-part questions so I solve first three parts. For the last part repost the question.

Q: a. How many different teams can be chosen if there must be exactly three male palyers on the team?…

A:

Q: Determine the radius and interval of convergence of the following power series. Σ sin k = 1 6 3 5k…

A:

Q: If C is a circle of radius 8 centered at the point (-1, 1), then evaluate f (7y - ein (2)) dz + (102…

A:

Q: Solve the equation. Give your answer in exact form. log4 (x+7) + log4(x-5) = 1

A: According to guideline we need to solve one question.

Q: Find the radius and interval of convergence of Σ2(x + 3)" n=0

A:

Q: If f (x, y, z) has continuous partial derivatives and S is a closed surface, show that მ2 f f [[ D.…

A:

Q: Simplify. Write your answer in scientific notation. (6.3 104) (2.3107) Show your work here Hint: To…

A:

Q: etermine from the graph whether the function has any absolute extreme values on [a, b]. Then explain…

A: Function is not continuous because there is a break in the given graph so we can easily observe…

Q: 3. Use the Integral Error Estimate to find N s.t. RN <0.00001 for the following series. That is, how…

A: For a series ∑n=1∞an . If Sn is its n th partial sum and Rn is reminder of n th partial sum then…

Q: Consider the following relation on R. For every x, y ∈ R, x ∼ y if andvonly if x −y ∈Q. (a) Prove…

A:

Q: Approximate the integral using the first four terms of Maclaurin series. (Use decimal notation. Give…

A: ∫00.9cosx1-xdx

Q: Let F(x, y, z) = xzi+yzj + xyk, Surface S is the part of the sphere x² + y² + z² = 4 that lies…

A:

Q: 2-6 Use Stokes' Theorem to evaluate ff, curl F. ds. 2. F(x, y, z) = x² sin zi + y2j + xy k, S is the…

A:

Q: At noon, ship A was 12 nautical miles due north of ship B. Ship A was sailing south at 12 knots…

A: