Show that V² (v-x) = 2V.v+x-V²v, where v is a vector field and x is the position vector of a point in a 3D space.

Q: (cos 3x - x²) (sin 3x-x³)5 dx cos² x (tan x) (sec² x - 1) dx

A: 1st question solved by substitution rule and 2nd question solved by identities rule.

Q: Prove both sides equal πU (PN ₂) = (π Up) N (π UV).

A:

Q: lim f(x) = x→3+ Is f concave up or concave down on 1 < x < 3? What is the absolute minimum of f(x)…

A: If the limit of x approaches a certain point from the right, then it is written as limx→a+f(x). If…

Q: Evaluate the integral ¹9(√x² + y²) dxdy.

A:

Q: 8. Solve the recurrence relation an = given do = 40, a₁ = = 37. 2an-1-an-2, n ≥ 2,

A: Given recurrence relation is an = 2an-1 - an-2 , n ≥ 2 given a0 = 40, a1 = 37

Q: 2. The subset [a,b) of R is neither open nor closed. Prove it and construc an illustration.

A:

Q: lowing data : x- f(x) : f'(x): 1 1 -5 0 1 1 3 7. the value of f(-0.5) from the (Anna B Togh 2005)

A: Given: x f(x) f'(x) -1 1 -5 0 1 1 1 3 7 To find f(-0.5)

Q: Let f be the function from {a, b, c, d, e} to {1,2,3,4} with ƒ(a) = 3, ƒ (b) = 1, f(c) = 2, f(d) = 4…

A:

Q: Given w = = f(x, y, z) = 4x² + y² + 42². Sketch the level surface of the function for w = 1.

A: The level surfaces of the function: w=f(x,y,z) results, when w=k slices the function: w=f(x,y,z).…

Q: Use three-point midpoint formula to evaluate the first derivative of y = x² + 4x − 5 at x = 0 using…

A: Given that y=x2+4x−5. We have to find the first derivative of y=x2+4x−5 at x=0 using a value of h=14…

Q: Which of the following is the isogonal trajectories of the one-parameter family of curves y(x-a) = 1…

A:

Q: Given the set P of all points in a plane, let M denote the set of all permutations of P that…

A: Given : set P of all points in a plane, let M denote the set of all permutations of P that preserves…

Q: x+2y-z = 2 2x + 2y + 2z = 12 x-y + 2z = 5

A:

Q: A student organization at Penn State is voting to pass its budget. Susan has 6 votes as the…

A: Given: Susan has 6 votes as the President, Joe has 4 votes as the Vice-President, Carol has 2 votes…

Q: Let A(1, 2, 1), B(3, 1, 2) and C(2, 1, 2) be points in R³. a) Find the point-normal form of the…

A:

Q: The following scatter plot represents the height of a basketball in seconds during a free throw…

A: 2. (a). The given scatter plot image resembles a downwards opening parabola which is the graph of a…

Q: 11. Find an orthonormal basis for the solution space of the following homogeneous system of linear…

A:

Q: Consider the equation 2x²y" - xy' + (x - 5)y=0 in some interval 0 < x < R. ty that x = 0 is a…

A:

Q: Evaluate the integral S CO|CT CT | CO CT /Co NIC 8 dx using the two-point Gaussian quadrature rule.…

A: We have to evaluate the integral ∫−22816+x4dx using the two-point Gaussian quadrature rule. Here,…

Q: 3. Give a geometric description of Span{V₁, V2, V3}. 8 (a) V₁ = 2 V₂ = 3 V3 8 (b) V₁ = 2 3 (c) V₁ =…

A:

Q: Determine the volume when the region, bounded by the given equations,

A:

Q: Define a linear operator (transformation) on R2R2 by performing the following operations in order:…

A:

Q: using an online graphing app, construct a graph which lie on the interval (-8,8) choose three…

A: F(x)=X^2-64 be the continuous function  -8&lt;X&lt;8 (a)  F(-8)=(-8)^2-64=0 (b) F(-8+0)=0=F(-8-0)…

Q: D H

A: In postorder we must first go to left then right and after that data.

Q: Consider the following hypotheses: He: = 8 HA: 8 The population is normally distributed. A sample…

A: Solution :-

Q: In the given figure, using Kruskal’s algorithm, which edge should we choose third? a. EF b. AG c.…

A: In Kruskal's algorithm, at a step,the edge with minimum weight is chosen if it does not form cycle…

Q: (b) o 24 dx, n=6

A:

Q: Which set of edges below is the minimum spanning tree of graph G? u 5 6. CO a Od 2 4 5 3 H S 7 E 2 6…

A: To find minimum spanning tree of given graph

Q: Suppose that a mass of 219 g stretches a spring 5 cm. If the mass is set in motion from its…

A:

Q: Sturm-Liouville differential equation in hy

A:

Q: Consider A= (0, 4, 2), B =, (6,-1,0) and C = (3, 0, 1). 1 (a) Find the unit vector having the same…

A:

Q: Use regression to find a quartic model for the given data set. Round the regression parameters to…

A:

Q: 12 12 None of the alternatives are correct · (1¹)) = If L <=lim In then f(t) is 042

A:

Q: Problem 5. (a) Show that if A = A-¹, then det(A) = ±1. (b) If ATA-¹, what is det(A)?

A:

Q: y JJ x² + x2 DA dA R: trapezoid bounded by y = x, y = 4x, x = 1, x = 4 y y x² + dx dy + dx dy x² +…

A:

Q: A total of $20,000 is invested in two corporate bonds that pay 3.5% and 5% simple interest. The…

A: Given:   A total of $20,000 is invested in two corporate bonds that pay 3.5% and 5% simple interest.…

Q: Consider the polar curves C₁ : r = 2 - cas 0 and C₂: r = 2 + 2 cos 0, 0 € [0, 27). 1 (1.) Show that…

A:

Q: Find a non-zero vector w E R4 which is orthogonal to all of the following vectors: -2 -3 2 -3 Enter…

A:

Q: Find the root of functions by Urimp Newton-Ropson Method •) f(x) = 2² ((x² +0.712) e 20.1x² -26X62,…

A:

Q: Find the Laplace transform of the following: 1. 4t + 12

A:

Q: 2. If f(x, y) = x² + xy − cos(xy), find the domain and range.

A:

Q: Consider A= (0, 4, 2), B =, (6, -1, 0) and C = (3, 0, 1). 1 (a) Find the unit vector having the same…

A:

Q: A firm faces the production function Q = 4K0.5L0.5 where K is capital and L is labor. a. Find the…

A: Note: As per our guidelines we are supposed to answer to only 3 sub-parts Q=4K0.5L0.5 where K is…

Q: Consider the curve segments: S1: y = x² from x == to x = 3 and 52: y = √√x from x = to x = 9. Set up…

A:

Q: Find the values of w,x,y and z in fraction form using a)gauss elimination, b) gauss-jordan…

A: Since you have posted a multiple question according to guildlines I will solve first question for…

Q: HHTH. What is the probability that the fair coin was selected? (8/81)(1/2)

A: Given that Beatrice has two coins. The first coin is fair and the second coin is biased. Thebiased…

Q: an open ball in the set X, with its radius & satisfying -d(x, a), Vx € X at the open ball Be (x)…

A:

Q: What is the equation of the slant asymptote of the rational function? f(x) = 10x³-15x²+x-1 5x²-2 11…

A:

Q: 5. Determine if each set is linearly independent. If the set is linearly dependent, give an example…

A:

Q: Find the characteristic equation and the eigenvalues (and a basis for each of the corresponding…

A: