a. 5ax at P(4, 120°, 2) b. 5a, at Q(3,4,-1) c. 4ax - 2ay - 4az at A(2,3 ess the unit vector ax in spherica . P(2,1 rad, 0.8 rad.) Dar

Q: Approximate fƒ(1, 3) using the contour diagram of f(x, y) shown below

A: Here, in the question, it is been discussed about contour diagram. We have to approximate the…

Q: Find the differential of ƒ(x, y) = √√x³ + y² at the point (3,2). df = Then use the differential to…

A:

Q: xt The function h(t)= -120 cos + 125 represents the height h, in feet, of a seat on a Ferris wheel…

A: Note: As per the honor code, only one question can be answered and up to 3 sub-parts only. Please…

Q: X1 X2 x3 X4 = Solve the system -27 -22 1 0 +s 14 12 1 O 4x1 -X1 3x1 2x1 -5x₂ +4x3 +4x4 = +x2 +2x3…

A:

Q: Consider the ellipsoid x² + 2y² + 4z² = 22. Find all the points where the tangent plane to this…

A:

Q: 2. cos xdy = -(sin x) ydx + dx

A:

Q: 2. Let G = {a, b, c, d, e} with the operation * defined by the table below. Determine if the system…

A: Let G be a set and * be a binary operation then (G,*) is a group if  (G,*) has closure property.…

Q: Find the center of mass of a thin plate covering the region bounded above by the parabola y = 4 - x²…

A:

Q: Z+ as follows: For a, b € Z+, a*b = a - b + 1. Z+? Explain. (3.1) Define an operation * on Is * a…

A:

Q: . Find the solution set of the following system by means of matrices: 2x-3y=-1 (11) x+4y=5 (111)…

A: We have given a system of equations. We need to find solution set for the given system of equation.…

Q: Determine the eigenvalues of the inverse of the following matrix 0-1 1 211 8-8-2 O 12, 12-1 2,-1,-2…

A:

Q: Find the relative extrema of f(x)=32x² - 4x³.

A:

Q: Let Sn = bk. Use the definition of s6 and your work in part (b) to write out an unsimplified…

A:

Q: S₁ dy h(y) g(x) dx =

A:

Q: Use Lagrange multipliers to find the maximum and minimum values of f subject to the given…

A: Given, fx,y,z=xyzx2+y2+z2=243 The Lagrange Multiplier is applied to find maximum and minimum values…

Q: V = {ax³ + ax² + bx − 2c|a + c = 0, b ≤ R} ≤ P3.

A: Solution

Q: 1. Determine for each of the following differential equations whether it is linear, separable, both,…

A:

Q: y = x + y, y(0) = 1.

A: From Euler method  dydx=fx,y we have  yi+1=yi+hfxi,yi for all i=1,2,.... Given y'=x+y,   y0=1 Here…

Q: Write the equation of the plane passing through P with direction vectors u and v in vector form and…

A:

Q: 1 3 28 (iii) Compute AB (iv) Compute (AB) 3) Let A = and B = -1 20 4 1 (i) Compute A - 1 - 1 (v)…

A:

Q: Adult movie tickets cost $12 each and student tickets are eight dollars each. What is the cost to…

A: Given that cost of movie tickets for an adult is $ 12 each Also given that cost of movie tickets for…

Q: Let L1: U → V and L2 : V → W be linear transformations, and let L = L2 ◦ L1 be the mapping defined…

A: It is given that L1 is the linear transformation from U to V and L2 is the linear transformation…

Q: Let S = {(2,0) = R² : 2 = R}. If lim f(x, y) = 0 then (2.9)-(0,0) f(x, y) = 0. lim (z.g)-(0,0)(8…

A:

Q: Use Lagrange multipliers to find the maximum and minimum values of f subject to the given…

A:

Q: Suppose that (n) is a Cauchy sequence such that än is an integer for all n E N. Prove that (xn) is…

A:

Q: Partial Derivatives. 1. Find the partial derivatives: fx, fy or f₂ f(x,y) = x sin (x - y) b. f(x,y)…

A:

Q: 4. The velocity of a particle which moves along the s-axis is given by v = 2-4t+5t, where t is in…

A: We use to formula :  a = dv/dt v = ds/dt in order to find s,v,a at t=3 s.

Q: (a) Use properties of quadratic functions to prove that 6(x - 1)² ≥² for all real x > 2. (b) Use…

A:

Q: n Let S := 1 ² ² + 1 =nEN } . n²+1 f S. Fully justify your answers! Prove that S is bounded and…

A: Given  set  S =  nn2+1 ; n∈ℕ  (.)  Bounded sequence :…

Q: Let f(x) be a fixed integer polynomial, and let m be a fixed positive integer. Denote the number of…

A:

Q: The population growth of a small country is described by the function P(t) = 60,000,000 1.020, where…

A:

Q: th

A:

Q: Please have a systematic way of solution (Question-Solution-Final Answer-Conclusion format) A. For…

A:

Q: Use Lagrange multipliers to find a vector in 3-space whose length is 6√3 and whose components have…

A: Formulate the langrangian . Use the multiplier λ.

Q: Problem 8. Let fg,: I→ R2 be given by f(x) = (0,r), g(x) = (1,2). a. Specify a homotopy h: Ix I→ R2…

A:

Q: (c) (d) In n (−1)” +00 n=1 2n³ 3 n + +1 +00 n=1 n

A:

Q: Problem IV Consider the set of a s. Determine whether it is a subspac 61. z-y +z = 0. 62. x+y+z= 1.…

A:

Q: Find the exact value that the sequencesin" 1 converges to. (Note n=0 that as usual, sin" x means…

A:

Q: V = {ax² + bx + 3|a, b ≤ R} ≤ P2.

A: Given: V=ax2+bx+3 | a, b∈ℝ⊂ℙ2 To write: The given set as span of minimum number of vectors.

Q: 4. dy dx (sin x) cos y (a) y(0) = 1 (c) y(3) = 3 (b) y(1) = 0 (d) y(0) = - 512

A: From the given differential equation we have to find the linear equation of x and y. We use the…

Q: Mini Exercise Solve this using big M method. max z = 3x₁ + 2x₂ + 4x3 + X4 subject to:

A: The given LPP is as follows  Max z=3x1+2x2+4x3+x4subject to…

Q: determine all eigenvalues and corresponding eigenvectors of the given matrix.

A: We know that a number λ is said to be an eigenvalue of the matrix A if there exists a non-zero…

Q: Suppose (X, d) is a metric space and E a non-empty subset of X. Prove that E is disconnected if and…

A: Assume E is disconnected. Then there exist two open set U and V in E such that 1. U∩V=∅ 2. E=U∪V 3.…

Q: n a population of 100,000 people, 40,000 are infected with a virus. After a person becomes infected…

A:

Q: Question 2 • Find the probability P(x ≤ 3) given the probability density function you identi- fied…

A:

Q: 3. Consider the surface defined by z = f(x, y), where: x²y 2(x² + y²) Write down the equation of the…

A: Note:-Our guidelines we are supposed to answer only one question. Kindly repost other question as…

Q: Let A = A 3 4] 1 2 Use t

A:

Q: 10. A college student sent a postcard to her parents with the message: SEND + MORE MONEY If each…

A: The given message contains two 4- digit numbers. Even if we take largest two 4- digit number…

Q: Problem 1. Considering the capital letters as unions ness, divide the letters into groups according…

A: the letter are divided into homeomorphism classes according to the number of holes. there are three…

Q: Use the big-θ theorems to find good reference functions for the following: f(n)=(n2 +5·2^n)lg(n^7…

A: Solution:     We know, n2 ≤ 2n , for n ≥ 4.     => n2 + 5.2n ≤ 6.2n     lg(n7.2n) = lg(n7) +…