For f(x) = S2x 3 for x < 1 for x ≥ 1 )' the value of 6 f(x)dx is

Q: Compute the partial derivative.

A: It is in the form of the :M dx+N dy+P dZP=18z

Q: Select all that is true with regards to the first order conditions of the Lagrange function…

A: The objective of the question is to find the first order conditions of the Lagrange function for the…

Q: i. Ing g on himur Con 4 f'(x) = 1 -2, x #0 -2,2 1 nd C

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Q: sider the following lines. r(t) = (3t+1,3t+2, 2t+1), for oo<t<∞⁰0 R(s) = (s+ 4, 4s+5, -5s+3), for…

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Q: (i) Show that A is diagonalizable. Find a basis of R³ consisting of eigenvectors of A. Write down an…

A: Since you have asked more than one question, find the solution of the first one.

Q: For each of the following functions, sketch it and decide whether it is even, odd, or neither: -1…

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Q: Find the eigenvalues and eigenvectors of the matrix 2 -9 -3 From smallest to largest, the…

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Q: K Prorate the following expenses and find the corresponding monthly expense. Lan pays a semiannual…

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Q: c. Which of the following sets of equations could trace the circle x² + y² = a² three times…

A: The circle x2+y2=a2The parametric equation at the point (0,−a)x=−asin(t),y=−acos(t)Since there are…

Q: Assume S is the surface x1000+y8000+z1000 = 10¹2 and f = (9+ eyz, x³yz, 3x - 5y - 6 cos(zx)).…

A: Here we use the Divergence theorem for a surface S inclosing a volume V

Q: 4. For an odd prime p, suppose that (=) = 1 and consider the congruence x² = a mod p. (i) For p = 3…

A: We shall be using basic results from quadratic reciprocity for solving this problem. And

Q: Given a (3 x 4) real matrix A and a (4 x 3) real matrix B, with determinant |(AB)| = a, and…

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Q: (Technology Permitted) Let R be the region bounded by y=In(x), y=0, x= e². a. Write but do not…

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Q: / /-1/-// 1/ 1 / 1

A: Clearly slope field is parallel to x axis at y=0,1Hence .dy/dx=0 at y=0,1Forms two factor…

Q: 3. Find the line integral fF.dr where C' is the circle of radius 5 in the xz-plane oriented…

A: The given vector field is .Find the value of line integral  as follows.The parametric surface can be…

Q: Let f(x) = x2, and compute the Riemann sum of f over the interval [3, 5], choosing the…

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Q: 5. Let A denote the set of all diagonal 2 × 2 matrices with real entries. That is, let A be the set…

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Q: Find the potential function f for the field F = 6x i + 6y j + 7z k. A general expression for the…

A: Note: As you have posted multiple question but I will answer first question according to the…

Q: Consider the function ƒ (x₁, x₂ ) = 5 x² + 4x² defined on (x1, x2 ) = R². Which of the following is…

A: The objective of this question is to find the Hessian matrix of the function f(x1, x2) = 5x1^2 +…

Q: Questions 12-14 refer to the following information: The velocity of a particle moving along a line…

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Q: Use the definitions to compute the unit binormal vector and torsion of the following curve. r(t) =…

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Q: E. Let F be the three-element set {0,1,♡}. Show that there are unique operations + and ⋅ so that F…

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Q: 2. Solve the integro-differential equation for f(t) t –2f(t) = 2 | sinh(w)f(t – w)dw + 1 2 f'sir

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Q: Factor f(x)=x^5-3x^4-6x^3+26x^2-27x+9, given that 1 is a zero of multiplicity 3.

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Q: Show that the function f(x): = √/x² is uniformly continuous ON A:= [1,00), but that it is not…

A: To show that f(x) is uniformly continuous on A, we use definition of uniform continuity and to show…

Q: 12. Assume the multiplication shown below is correct except for the placement of the decimal point…

A: Note that on the LHS we have a whole number . This fact needs to be kept in mind.

Q: Evaluate the surface integral F. ds for the given vector field F and the oriented surface S. In…

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Q: A solid cube in the first octant is bounded by the coordinate planes and by the planes x = 1, y = 1,…

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Q: 14. Q = /5 16. Q = 2= [₁ 1-2 21 32 -2 3

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Q: f(0) = 0, f'(-2) = f'(1) = f'(9) = 0, lim f(x) = 0, lim f(x) = -0, X-6 f'(x) 0 on (-2, 1) and (6,…

A: - The function starts at, has critical points at , , and , and approaches zero as goes to…

Q: Find the value of integral 2+1 (y² +ix) dz

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Q: Consider an equilateral triangle of side 2 units. Looking at the 30-60-90 triangle made by the angle…

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Q: The trace determinant plane in our textbook (and in We- bAssign) includes two border cases: (1) when…

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Q: Solve the system of differential equations Jx'= -6x -2y \y'= 3x – 1y x(0) = −2, y(0) = 3 The lesser…

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Q: You need to pay attentien on this one. I want you to find the interval of convergence for the…

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Q: A camera shop stocks eight different types of batteries, one of which is type A76. Assume there are…

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Q: Solve the heat equation U₂ = cu xx on the domaion 0 ≤ x ≤ 3, t > 0, u(x, 0) = ³ - ³x², ux(0, t) = 0,…

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Q: Find the work done by F over the curve in the direction of increasing t. F = 4zi + 4xj + 4yk, r(t) =…

A: Note that : Since you have posted multiple questions, we will provide the solution only to the first…

Q: Write the bordered Hessian matrix H of second order partial derivatives evaluated at the stationary…

A: The objective of the question is to find the bordered Hessian matrix H and its determinant for the…

Q: 1 + x 24

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Q: We say that a set A is numerically equivalent to a set B if there exists a bijective function f : A…

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Q: dR D₂CA0 1 dt OcPc R-R²/Ro) t = Step 9: Integrating with limits R = Ro at t = 0, the time necessary…

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Q: Find the mass and center of mass of the lamina bounded by the graphs of the equations for the given…

A: Solution:Given that, find the mass of the lamina and center of mass:

Q: lem #2: SSC (curl F) · ndS wher Use Stokes' Theorem (in reverse) to evaluate F = 4yzi + 8xj +9yzek,S…

A: Here by using Stoke's theorem we have to evaluate the given integral in the portion of given…

Q: Let's change the signs a bit: M' = aM - BMH H' = XH - MH This is no longer a model for a…

A: The model represents the population of two preys (or two predators) sharing the space and food…

Q: Find the exponential Fourier Transform of the given function and write the function as a Fourier…

A: Due to insufficient information of the second part ,we will solve only the first part. Kindly repost…

Q: Consider the following matrix: 2 -2 4 6 6 A = -1 1 3 2 -3 -1 1-3 -3 1 Give a basis for each of…

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Q: - Evaluate S using upper and lower sums. HINT: x³ dx b4-a² = (b³ + b²a+ba² + a³)(b − a).

A: Using the Upper Riemann sum and the lower Riemann sum we shall solve this problem .

Q: 3. Find the general solution to the vector DE ² = (1 ²¹2) ² + (-2²) using the method of variation of…

A: 3.The given system of differential equation is .Find the solution of the system as follows.The eigen…

Q: 48. Evaluate the surface integral. [12xz ds S is the part of the plane 2x +2y+z=4 that lies in the…

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