Use Stokes' Theorem to find the circulation of F = 5yi + 3zj + 6xk around a circle C of radius 7 centered at (5, 2, 7) in the plane z = 7, oriented counterclockwise when viewed from above. = [ ² C Circulation = F. dr =

Q: 10. use. Σn'e™** Use any test to determine whether "=1 converges or diverges and state the test you

A:

Q: 9. Decide if the following functions are bijections. Prove your answers. (a) f(x) = x³ - 1 (b) g(x)…

A:

Q: a. Find the normal vector to the tangent plane b. Find an equation of the tangent plane to the given…

A: To find normal vector to any curve at any point we need to find it's gradient, also equation of…

Q: Find the absolute maximum and minimum of the function f(x,y)=2x² - 4x + y² - 4y + 3 on the closed…

A:

Q: Select the following relations on Z that are equivalence relations. O{(a,b)|a>b-1} {(a,b) | a² = 6²…

A:

Q: 1. Sketch a graph of y = 3 cos (x − 2ñ) — 1. - -

A:

Q: Below are given examples of an interval, [a,b], a function ƒ : [a, b] → R and a partition P of [a,…

A:

Q: a. Solve the system u = 3x +2y, v=x+ 5y for x and y in terms of u and v. Then find the value of the…

A:

Q: Use the method of undetermined coefficients to solve the given nonhomogeneous system. *- (-:-) x +…

A:

Q: A) Find the contour integral z²dz when C is a parabolic part y = O(0;0) to point P(1;2) P(1, 2)…

A:

Q: Calculate the singular value decomposition A = UEVT of √2 3 A = -3 0 Σ = V = ab U = ab sin (a) sin…

A: The columns of V are the unit eigenvectors of  ATA. The diagonal element of the matrix sigma are the…

Q: b) Prove that G = K2,12 is planar by drawing G without any edge crossings. (c) Give an example of a…

A:

Q: Let un be the sequence in 12 with 1 in the nth place and zeros elsewhere. Prove that the set {u} is…

A: un=0,0,......,0,1,0,..0.. ∈l2             1 is in the nth placeLet S=u1,u2,u3,....... ∈ l2Note that…

Q: Let f: Z → Z be defined by f(x) = x² + 1, and let C = {1,2,3}. Find f(C), f-¹(C), f-¯¹(ƒ(C)) and…

A:

Q: 10. Let f(0) = 0 and f(x) = 1/x for all x € (0, 1]. Show that f is not integrable on [0, 1] by…

A:

Q: Q17. Suppose M is a stochastic matrix representing the probabilities of transitions each month.…

A:

Q: Use the age transition matrix L and age distribution vector x₁ to find the age distribution vectors…

A: Given: Age transition matrix, L=022014000010000140, Age distribution vector,x1=100100100100To find:…

Q: (b) The decomposed Laplace Transformed of y(t) is given by OA 41 S-2 1 +4 (S-2)2 +1 (S-2)² +1 O B.…

A:

Q: Give three equivalent properties of conservative vector fields. Consider the vector field F defined…

A:

Q: s(t)=²-3t²+2t (a) Find the velocity function of the particle at any time t 2 0. v()-21-61 (b)…

A: As per the guidelines I have solved three sub parts .Answer is given below.

Q: Calculate the below contour integral. (Hint: Use Cauchey's integration formula) $ |z|=2 dz z³(z + 4)

A:

Q: Find the solution to the following system of equations. z' + 4y = 0; y(0) = 1, and z(0) y' + z = t₁…

A:

Q: B = M - 5C2  making C the subject of the equation we get C =

A: Change the subject of a formula is the variable that is expressed in the form of another variable…

Q: U B BD □AC CE 0 BE AE CD AD ⒸAF OCF 15. AB ODE ODF BC BF EF 10 Find the minimum cost spanning tree…

A:

Q: Use the method of cylindrical shells to find the volume generated by rotating the region bounded by…

A: Solution :-

Q: • S (x + 6√Y) ds ds where C is given in the accompanying figure. Evaluate √(x+6√y) - (Type an exact…

A: Given ,              ∫C  x+ 6yds where C is given in the accompanying figure .  Now first we find…

Q: The point x = O is a regular singular point of the given differential equation. Find the recursive…

A:

Q: Recall that an integer m is a square if m= k² for some integer k and is a triangular number if m =…

A: This is a classic application of pells equation. We first transform the equation into a pells…

Q: 3. The trigonometric equation cos²x- sin²x = 0 has the same solutions as the trigonometric equation…

A: In the given problem we have to show that two trigonometric equation has the same -solution.  If we…

Q: In xdx For the integral J₂2 to have an Error using Simpson's Rule of less than or equal to 0.001,…

A: We find the number of subdivision in Simpson method to approximate the integral

Q: 3. Compute the integral of f(x, y) = y = eva 1/lny over the domain D bounded by y = e and

A:

Q: Suppose F(x, y) = (x² + 3y, 7x − 7y²). Use Green's Theorem to calculate the circulation of F around…

A:

Q: Use Green's Theorem to find the counterclockwise circulation and outward flux for the field F and…

A:

Q: Suppose that a thin metal wire in the shape of a semicircle occupies the curve C, where C is the top…

A: The given problem is to find the total mass of the wire where the thin metal wire bent in shape of…

Q: Answer each question part, showing your step-by-step workings to reach the  conclusion. ax+b=c…

A:

Q: The average number of cigarettes smoked per person in a year in the top ten countries for smoking…

A:

Q: b) Give an example to show that the product fg need not be uniformly continuous.

A: Given: f:A→B, g:B→C are uniformly continuous.To show: b) The product fg need not be uniformly…

Q: Find the La Place transform of the function f(t) = t cos t 5 (s² + 1)² s² + 1 (s² + 1)² 2S-1 (s² +…

A:

Q: Q4: Sketch the phase plane portrait of equation (without explicitly computing its solutions),…

A: As per the question we are given a dynamic system governed by the following 2nd order linear…

Q: Show that the differential form in the integral below is exact. Then evaluate the integral.…

A:

Q: For the series (-1)" 9n0.8 +4 calculate the sum of the first 3 terms, S3. S3 Include several…

A:

Q: A force of 33.9 N is applied tangentially to a wheel of radius 19.9 cm and gives rise to an angular…

A:

Q: Jady has 24 coins, some nickels, some dimes, and some quarters. He has 4 more nickels than dimes,…

A:

Q: Which one is the solution to the given iterated integral? (Hint: polar coordinates) L'S√²-²…

A: We have to find the value of given double integral.

Q: Jai builds a sculpture with three separate parts, shown in the models below. Each part is made of…

A:

Q: Apply properties of congruence to make computation in modulo n feasible. Find the unique r such that…

A:

Q: Consider the simplex tableau given below. X₁ X2 X3 S₁ S2 S3 Z -5 0 1 2 0 0 -5 -5 0 2 5 0 2 1 0 0 5 0…

A:

Q: Find all the absolute extrema of f(x, y) = 3 + xy - x + 2y on the region bounded by x = 1, y = -x +5…

A: The given problem is to find the all absolute extrema of function f(x,y)=3+xy-x+2y on the region…

Q: Select the following statements that are true. A and B are arbitrary sets. The cardinality of…

A:

Q: 1. Determine the eigenvalues and the associated eigenvectors of each of the following matrices.…

A: In the given problem a matrix A is given. We have to find the eigen value and eigen vector.  If the…