4. Let f(x)=√√2 cosx - x (a) Determine the absolute extrema of the function f on the interval [플,플]

Q: 1.) Give the Fourier transform of the function f. Sx ha x = [0, 1] f(x) = 0 otherwise.

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Q: too 3. let e* = + 38 = 1₁1 nào n a) Find a power series for tet? 6) Integrate the power series…

A: Given series is ,                        et  =   ∑n=0+∞tnn! Then the power series for  tet2  . (.)…

Q: Solve e PDE using Fourier series () Derive and solve the BVP (bi Solve the other DE and write down…

A: Here we need to use Fourier series to solve given problem.

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Q: Recall that the Gaussian integers Z[i] is the following subring of C: Z[i] = {a+bi a,b ≤ Z}, where…

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Q: Use the definition of set operations to prove that for any set A, A- A = Ø . A + A = Ø

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Q: The following are the cores of 23 students in a 50-item test. 26 28 32 45 38 47 36 35 30 40 29 50 43…

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Q: Use trapezoidal rule to approximate the integral f√3+2x³dx; n = 6 O 11.50676706 O 11.20676706 O…

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Q: What is the x-coordinate y = 2x + 1, x + y = 7, and x = 8? 05 7 8 ΝΑ of the centroid of the plane…

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Q: Evaluate the following [8(t+ 3)e¹dt 88

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Q: Evaluate J by means of trapezoidal rule using n = 10 and n =20: 1 = [*exp(-x²) dx Evaluate J by…

A: We need to find the value of J=∫01exp(-x2) dx using the trapezoidal rule with n=20 and n=10

Q: 38. Which of the following nodes should be the root of Tree A so that nodes B and I will be of the…

A: 38

Q: (a) Consider the initial value problem dy X ; y(0) = 1. dx Y Verify whether conditions for existence…

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Q: 20. Find the volume of the parallelepiped with adjacent edges u = (-2, 0.75, 4), v = (6, -0.3, 8),…

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Q: Referring to Figure 11, suppose that fr F-ds=4n, fo F.ds = 4T Use Green's Theorem to determine the…

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Q: Prove using direct proof. Include explanation.   If n is an even integer, then 7n + 4 is an even…

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Q: 3. Imagine you fill your bathtub up at a rate of 2 gallons per minute. This means that every minute…

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Q: (2) Let x, y and z be real numbers. Show that the distance between a real number x and z is the sum…

A: Let us solve the given problem geometrically in the next step.

Q: -2x² Find the absolute extremum values of f(x) = xez 3 (Note: e 2≈ 0.22) on the interval [0, 1].

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Q: Problem 10. Consider the following set of polynomials in P₁: S = {1+ 3t² +t³, 1+t+ 2t³ + 3t¹, t+t² +…

A: We know that two vectors are linearly dependent if one vector can be written as a scalar multiple of…

Q: (4) Let A be a nonempty subset of a bounded set B. Why does inf A and sup A exist? Show that (a) inf…

A: If S is a non-empty subset of real numbers and bounded above .Then S has a supremum that is supS…

Q: с рое избиј using Fourier series (a) Derive and solve the BVP, T, 4)= (bi Solve the other DE and…

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Q: What is the volume in cubic units of the solid formed when the region bounded by y = 3x - x^3,…

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Q: (b) Find the largest eigen value and the eigen vector for the matrix A = x¹ (0) = (1 1) 1² il where

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Q: Linear Systems. (a) Find the solution set of the homogeneous linear system below. x + y + 2z = 0 y…

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Q: What is the volume in cubic units of the solid formed when the region bounded by y = x^2, y = 1, and…

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Q: Use Taylor series method to compute x(0.2) and given that d²x dx dx --4x = 0 ,x (0)=1, (0)=2 dt dt…

A: We can solve this using Taylor series of numerical method

Q: Question 6 Obtain the power series solution of the differential equation y" (1+x)y=0 about the…

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Q: Obtain the power series solution of the differential equation y"-(1+r)y=0

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Q: draw the solid x² + y² +Z²- √3x² +31² 2:

A: Any point in the three dimension can be represented by the point: x, y, z. Use a graphing utility to…

Q: 2. The position of a particle moving horizontally is given by s(t) = t 6t+ 9t + 4, where s is in…

A: Given that, s(t)=t3-6t2+9t+4 As we know that when particle changing the direction its velocity…

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A: Solid R

Q: olve the following differential equation y" + 3y' + 3y = et sint, y(0) = 0, y'(0) = 1

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Q: A particle moves in two dimensional space where i and į are unit vectors in the x and y directions…

A: given  r→=6t-4t2i^+2t j^ a) write down the particle's velocity vector in component form. ii) find…

Q: 4. Find the center and the radius of convergence of the following power series. 00 2100n n! zn

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Q: 6. Let U = {2,4,5,6,8,9,10} Y = {yly = 0.5U} Enumerate: a.) P(X U (YOZ)) X = {x | x² 13x + 42 = 0} Z…

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Q: Consider the following linear programming problem; Max. X0 = 3 x1 + 4 x2 Subject To: 2 x1 + 6 x2 ≤…

A: After introducing slack variables Max Z =   3 x1 + 4 x2 + 0 S1 + 0 S2 subject to…

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Q: For item 4, illustrate the problem, the triangle diagram, and solve for the problems.  4. A Three…

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Q: 1 1 = 5° 0² J exp(-x²) dx

A: Using trapezoid rule

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Q: 40.If Tree A is rooted at node E, what will be the height of node C? Tree A A. 3 C. 1 B. 2 D. 0

A: 3

Q: Find the general and Singular Solution of the Following differential equation x²= 1 + P²

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Q: What is the volume in cubic units of the solid formed when the region bounded by y = x^2 + 1,…

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Q: Q4) Find the largest eigen value for the matrix 2 T A with x (0)=(7/17 1) 54

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Q: Fournier series, given the function f(t)= x-x^2, -π≤x≤π (a) find the coefficient a5, and (b)…

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Q: Is the slope of the line tangent to the curve the derivative?

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Q: Use local linear approximation to estimate In (0.99

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Q: section method to

A: Given,         f(x)=x-cos(x);     0, π