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Q: Find the minimum  of the function f(x) = 2x3 + 3x2 − 12x + 17

A: We have to find the minimum of the function f(x)=2x3+3x2-12x+17.

Q: 2. Solve the following partial differential equation au/2 = ²4/ 0x² du at u(0,t)=0. u(10,t)=100…

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Q: Suppose Cn is a segn of real numbers such that lim 1c₂1h exists and is non-zero. If the ROC h-00 of…

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Q: -5) as golve: x'= -3x + 3y +z -1 (**) x-sy-32 +7 2'=-3x + 74 +32-7 =) i) Does (**) have a solution…

A: As per norms, we will be solving only one question. If you need an answer to others then kindly…

Q: convert the following differential equation into a Perfect equation and then Find its general…

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Q: . (1-z)-¹

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Q: ex² dx dy dy dz dx Jy/2 [[6²² 2y

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Q: n Σ tan(kx) tan ((K+1)x) K=A

A: Given,           ∑k=1ntan(kx)tan(k+1)x

Q: Which of the following integrals correctly solve for the magnetic flux passing through the surface…

A: We can solve this using magnetic flux formula

Q: 2- Perform the following inverse Laplace transform using convolution theorem: 3s +1 C-1 S² + S

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Q: Let A be a set and let a € A. Suppose that f: A→ A satisfies (a) a = f (a), (b) if x Ey then f (x) =…

A: Given: f:A→A a) a∈fa b) fx∈fy To find: Solution

Q: Q.3 Solve the heat equation: ************ U,=U.. U_(0,t)=0, U,(7,1)=0, U (x,0)=3-3cos2.x, *********…

A: The given problem is to find the solution for the given heat equation partial differential equation…

Q: Set up the iterated triple integral that will give the following: = 4 (a) the volume of the solid in…

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Q: Find a plane that contains S and is perpendicular to the plane that contains the points

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Q: Let B (x, y, z) = (xz, yz, 3x² - z²). 1. The task is to identify the work done by B on a particle…

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Q: 31-35 Analytic Functions. Find f() = u(x, y) + iv(x, y) with u or u as given. Check for analyticity.…

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Q: (c) Given the set T := {(x, y) = R²: |xy| ≤ 1}. Is T a compact set? Show your working. If you say it…

A: (D)  Suppose A = ∪αα∈A be any open cover of S∪T.so , there is a finite subcover A1⊆A of S and…

Q: Find all integers n > 1 such that 1” +2^ +...+(n − 1)” is divisible by n.

A: We have to find the all integers n>1 such that 1n+2n+.........+n−1n is divisible by n. Firstly,…

Q: 1 0<x< 1/ 9=2-1<x<** (b) Find Fourier cosine transform of f(x) = {

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Q: = Solve the recurrence relation an an = an-1+2" with ao = 4.

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Q: 258. Are the lines of equations and x = −2+2t, y=-6, z = 2 + 6t x= -1 +t, y = 1+t, z=t, t€ R,…

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Q: We have verified that x² and x³ are linearly independent solutions of the following second-order,…

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Q: 2. Evaluate dx dr da Use Jav d. 2/x +3+ a Mr+1 +1

A: We need to evaluate the given integrals. formula for integral ∫1x+adx=ln|x+a|+C

Q: Define the function, period, then determine the Fourier Series of the periodic functions below:…

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Q: 11. Suppose that a firm that uses 2 inputs has the production function f(x1, x₂) = = 12xx and faces…

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Q: Find the feasibility region bounded by the following systems linear inequalities. Find the critical…

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Q: Confirm by multiplication that x is an eigenvector of A, and find the corresponding eigenvalue. 1 1…

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Q: Determine (without solving the problem) an interval in which the solution of the given initial value…

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Q: 2. Suppose that z is a function of a and y, and F(x2 - y2, xy - 2², yz - 2²) = 0. Calculate and…

A: Solution :

Q: Consider the following families of sets indexed by the set of natural numbers. Which among these is…

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Q: Use Runge-Kutt method to solve the following D.E.

A: Given the differential equation                      y'=1+y2+x3;  y(1)=-4, h=0.01 To find:…

Q: Consider the sequence of functions {f} defined on the interval [0, 1], where fn(x) = nx Evaluate lim…

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Q: Suppose that a 4 x 4 matrix A has eigenvalues ₁-1,A2-6, 3-7, and 14--7. Use the following method to…

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Q: 6. [s] Set up only a triple integral that will give the following: (a) the volume of R using…

A: Only draw the solids by hand.

Q: What is the basis and dimension of M3(R)?

A: Basis: For a vector space V, the set of linearly independent vectors that generate the whole vector…

Q: Use Euler's method with step length h = 0.5 and determine an approximate value for y(3) for the…

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Q: 6. Prove that for all n E w, the equality 0 n = 0 holds.

A: We will prove by induction. We need to prove for all n∈w, the equality 0·n=0 holds Let n=1, then,…

Q: 7. Before we formulate the problem make one reminder: A function f is quasiconcave if and only if…

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Q: 2. y4y² = 1; M(1,0). -

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Q: which sketch is a cross-section in the x-direction (L to the y-axis)? Why?

A: Sketch -1

Q: Lny) dx + (x-Lny) d y =o

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Q: Problem 4. (. Let C be the curve given by parametric equations x(t) = t², y(t) = 2t, z(t) = lnt, t€…

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Q: Use LU decomposition method to solve the system of equation. (Show your solution) X1 + x2 + x3 = 1…

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Q: (a) True or false? If you state true, then prove it, otherwise provide a counterexample. Given A, B,…

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Q: Using Bisection method find the solution of T g(x) = 2x - 3 sin =8 Use as initial values 3 <-T 2 2n…

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Q: Calculate the integral Sy3dx + (x3 + 3xyl)dy in the following ways; A) in shape direct. B) using…

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Q: PART#A Use Stokes' Theorem to find the circulation of F = (zy, y, z) around the boundary of the…

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Q: The set S=[1,3) is not compact. Which open cover of S contains a finite subcover? ○ { [1, 3 + 1/n) |…

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Q: 2. 3. NOR A NAND A OR A AND A NOT A NOT A NOT B NOT B NOR A NOT C NOT C MAND B NAND A

A: Theory: OR gate: A OR B ⇒ A+B AND gate A AND B ⇒A.B NOT gate NOT A ⇒A' NOR gate: A NOR B ⇒ (A+B)'…

Q: a) Show that F is conservative while G is not. b) Evaluate GdR, where C3 is defined by R(t) = tî +…

A: This is a problem of vector calculus.