Find The general Solution of VO (3y cosx + 4x + 2x² e^²) dx +(3 Sinx + 3) dy

Q: For the following function known as the "logsumexp", ƒ(x) = log Σ²_₁ exp(x;). (a) When p = 2, use…

A: The question provides a function f(x) called "logsumexp" and asks to show that it is convex using…

Q: Find the critical numbers, the intervals on which f(x) is increasing, the intervals on which f(x) is…

A: 1.If f1(x)>0 then f is increasing on the interval2. If f1(x)<0 then f is decreasing on the…

Q: 8) At a small university, there are 90 students that are taking either Calculus or Linear Algebra…

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Q: Set up all surface integrals required to integrate on the boundary of the box {(z,y,z) |1 ≤x≤2, 0≤ y…

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Q: W₂ is yz - plane: W₁ = {(x, y,0): x, y ≤ R} W₂ = {(0, y, z): y, z = R} -n V is not the direct sum of…

A: V=R3  and  W1 be the xy-plane and W2  be the yz-plane defined by             W1={(x,y,0):x,y∈R}…

Q: Let z 2i and w = 3-i. Locate the numbers 2z+w, z - 3w vectorially. =

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Q: (3) By using the Laplace transform, solve the DES y" + 4y' + 4y = e¯t, y(0) = 1, y" + 4y = tus(t),…

A: 3) The differential equation is given as ⇒y''+4y'+4y=e-t             with        y(0)=1, y'(0)=0.…

Q: Diagonalize the matrix A = -1 3-4 -2 3-4 1 1 3 Verify that AS = SA. Note that the some of the…

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Q: Use partial fractions to find the power series of the given function and find the interval of…

A: we have given a function f(x)=10(x2+1)(x-3) We have to use the partial fraction and then write the…

Q: Estimate the area under the graph of f(z)-cos(z)t (a) et endpoints ANSWER (b) right endpoints ANSWER…

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Q: estion 5 of 7 Use spherical coordinates to calculate the triple integral of x² + y² + z² f(x, y, z)…

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Q: 10y" 32y + 25.6y = 0 -

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Q: Consider the following. f(x, y, z) = 2x z=1-x² XX (a) Express the triple integral Lil y+z=2 (b)…

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Q: Consider the problem minimise f(x1, x2, x3) = x² + x²x² + 2x1x2 + x² +8x2 subject to 2x1 + 5x₂ + x3…

A: The reduced gradient is a vector of the first-order partial derivatives of a function with respect…

Q: 5. Solve the following initial value problem with r₁(0)1 and ₂(0) - 0. 2x1-x₂+4-1² -1 + 2x₂ +1

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Q: Consider the nonlinear system x'= x - xy y' = y + 2xy a) Find all critical points of this system. b)…

A: x'=x-xy , Let f(x,y)=x-xy y''=y+2xy , Let f(x,y)=y+2xy

Q: For Exercises 2 through 6, prove that T is a linear transformation, and find bases for both N(T) and…

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Q: Evaluate the triple integral. SIS. x dV, where E is bounded by the paraboloid x = 8y² + 8z² and the…

A: The integral is ∭Ex dV. where E is bounded by 8y2+8z2=x, and x=8. To Evaluate: the above integral.

Q: se Geogegra or your favorite software to graph the surface x³ - 3x + y² + 2y2. Then use s to find…

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Q: Use a change of variables to evaluate the following integral. SS Sxy dv: xy dV; D is bounded by the…

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Q: Use the shell method to find the volume of the solid generated by revolving the shaded region about…

A: Volume of solid by using shell method. The volume of the solid generated by revolving the region…

Q: Find a particular solution of the indicated linear system that satisfies the initial conditions x₁…

A: System of linear differential equations  Advance maths

Q: Find the intervals on which f(x) is increasing, the intervals on which f(x) is decreasing, and the…

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Q: Given the following table, find the average time for each element. Write your answers in order from…

A: To find the average time for each element, we simply add up the times for each trial and divide by 2…

Q: find dy/dx Lux. =√x.

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Q: QUESTION 4 A = [ Z₁ Z₂ Z3 -Z₁ ] (4.1) Find a necessary and sufficient condition for A to be normal.…

A: (a) The given matrix is: A=z1z2z3-z1∈M2×2C Now, firstly find the transpose conjugate of the given…

Q: Exercise 1: Non-uniqueness of spanning trees Find two non- isomorphic spanning trees of K4. Prove…

A: The given in the question is the graph K4, which is a complete graph with 4 vertices. The objective…

Q: One application of diagonalization is finding an explicit form of a recursively-defined sequence-a…

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Q: Consider the graph 6 = { [a], [b], [C], [d], [a,b], [b.c], [cid], [a,d], [o.c]} a) what is the…

A: Pre-requisite Knowledge:. The clique complex of a graph is a simplicial complex whose faces…

Q: Joive the following logarithmic equation algebraically. log_(4)(x)+log_(4)(x-2)=log_(4)8

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Q: After t days, 7 grams of iodine-131 decays to a mass y (in grams) given by t/8 y = 7 (²) ²²₁ ,t20.…

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Q: The initial tableau of a linear programming problem is given. Use the simplex method to solve the…

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Q: Set up all surface integrals required to integrate on the boundary of the solid {(x, y, z) | x² + y²…

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Q: Consider the slope field below for a differential equation. Use the graph to find the equilibrium…

A: Given that the slop field in the graph (see in question) for a differential question. We have to use…

Q: 1. Reduce each of these quantities to a real number: (a) 1 + 2i 3- 4i + 2-i 5i ;; 5i (1 - i)(2 — i)…

A: Given that the complex numbers a  1+2i3-4i+2-i5i b  5i1-i2-i3-i c   1-i4     .

Q: Let A € Rmxn, B € Rmxp be any matrix. Solve the following problem _min_ ||AX – B||2/17. XERnxp Hint:…

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Q: Number of Facilities 9 X 11 16 21 27 30 Average Distance (miles) 1.67 1.13 0.83 0.62 0.52 0.46 (c)…

A: The second-degree model is given by y=a+bx+cx2. The normal equations are given by:…

Q: Consider the three points (2, 2), (4,4), and (6, -2). (a) Supposed that at (2, 2), we know that f =…

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Q: a. Find the equation of the tangent and the normal line to the curve r+tan (ry) - 2 at the point…

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Q: BEC zw. w-1 (iii) Arg w and arg w. -√3i. Find the following: Let z = 7+3i and w = -1 –

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Q: Find all values of k for which the matrix A. k = 1 only B. all k = 1 c. k = 0 only D. k = 1, 2, or 3…

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Q: function V(x,y,z) = x² + xy + yz and a vector A = x² + xy + yzź are given. a) Find VV(x, y, z). b)…

A: Given function v(x,y,z) is

Q: 6. For each of the following curves: sketch the graph of the oriented curves, find x'(0) and add a…

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Q: (2) Describe the region whose area is given by the integral π/2 sin(20) // r drdo.

A: The given in the question is a double integral that describes an area in polar coordinates.…

Q: Use the distributive property to rem -(-v-w+6)

A: It is given that  rem -(-v-w+6). Objective:  To use the distributive property to  rem -(-v-w+6).

Q: b) f(x, y) = ln(xy) + √x-y + In(62²-52-6) √1-v-2y² d) f(x, y) = √1-y + √1-2² +In(16-2²-4y²)

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Q: Consider the following. the volume of the solid that is enclosed by the cone z = √√√x² + y2 and the…

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Q: Discretize the differential equation y" +8ty' +3y=2t, y(−1)= 1, y(0) = −1 with step-size = 1

A: Given: y''+8ty'+3y=2t y-1=1 y0=-1 h=14 To find: Discretization of the differential equation with…

Q: Select all of the functions for which Newton's method fails when using an initial guess of xo = 1. ☐…

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Q: 1) Of 15 students in a stats class, 8 are math majors, 6 are CS majors, and 7 are in education. None…

A: The principle of inclusion-exclusion is a counting technique used to find the number of elements in…