Let f(t) = 2t² for -4 < t <4 and extend periodically. Compute: f(1) = f(5) = f(-4.5) = f(-8)= f(12) =

Q: Q2) Let(M₂ (R), +..) be a ring. Prove H = {(a) la, b, c = R}is a subring of (M₂ (R), +,.).

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Q: Convert the following degrees to radians. a) 30° b) 175° c) 150° d) 315⁰

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A: Given: φn=2LsinnπxLφ2=2∂Lsin2πx2L To find: Solution

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Q: EX. 26 Let G be a group in which x² = e for all x € G. 1. Show that G is abelian. 2. Deduce that…

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Q: 4. ABP is a triangle, M is a point on AP. AB = a, AM = 26, and MP = b. N is the midpoint of BP. C is…

A: Follow the steps.

Q: T-M₂R)→R² Find the linear transformation whose matrix ~ = [ ²2 Мор=

A: T:M2×2ℝ→ℝ2 MT=10-112-11-1

Q: a) Let f: R" → R be a function given by f(₁,₂)=1..., where = 1. Show that the maximum of f(11,…

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Q: 2) Perform the following index shifts: i. Write y = no anx" as a series that starts at n = 2 ii.…

A: According to our guidelines we can answer only three sub-parts and rest can be reposted.

Q: Use bisection method in solving for the root of a function e^(-x) - tan x = 0. The guesses are 0.5…

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Q: Given that the equation below has a solution of the form y = ert, find r y'' – 12y' + 36y = 0 r =

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Q: (2 − x²) y" + 2xy' – 2y = 0 (a) Verify that y = x is a solution to the above equation. (b) Find the…

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Q: A plane with the equation + / + ² = 1 (a, b, c > 0) together with the positive coordinate planes…

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Q: Find the minimum and maximum values of the function f(x, y, z) = 5x + 2y + 4z subject to the…

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Q: Let ABC be a triangle with AB = AC. The angl meet the sides BC and CA at D and E, respectively. Let…

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Q: Find the quotient of B/A. Use pivotal method in solving for ALL (3x3, 2x2, ...) determinants. 3 1 3…

A: given, A=3137077468328491, B=45675678678978910 B/A=BA-1A-1=1Aadj(A)let adj(A)= C for get the…

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

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Q: 4. The position of a particle at time t is given by x(t) = 5+4 sin(t) y(t) = 2 − 4 cos(t) 0<t</ (a)…

A: This is a problem of parametric curve and Integration.

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Q: (D²-2D+5)y=e* cos x

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Q: Q1: Find the general solution to the following differential equation: y" - 2y' + y = x² - 1

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Q: Consider the function T:R² → C defined by T(x,y)=x+iy. Show that this is an isomorphism of real…

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Q: Question 2: Determine the nature and stability of the equilibrium points of the system dz = z-y+z²,…

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Q: 1) Write down the first 5 terms of each of the following sequences: {bn}a_1, where bn = nth digit of…

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Q: 15 Differential equations Please help solve Thank You.

A: Solution:-

Q: Find the power series of f(z) = z²ez, where |z| = 1.

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Q: Solve. The same way to ask the solution Find the general solutions of the system. www 0 4 x- 1 X 0 1…

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Q: 5. Using the least squares approximation, the best fit an exponential curve yea(x-b) to the given…

A: This is a problem of exponential curve fitting.

Q: Write an equation for the function graphed below 1 -3 -2 4 5 6 -1 - 2 3 I

A: The ratio of two polynomial functions when the denominator polynomial is not equal to zero is called…

Q: Suppose the function f: R→ R has Fourier transform 1 f(p) = e-p². 1+ 4π²p² i. What is the Fourier…

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Q: The coefficient matrix A below is the sum of a nilpotent matrix and a multiple of the identity…

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Q: 41. Vertex e is OA) an incident vertex OB) insecure vertex OC) isolated vertex OD) adjacent vertex

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Q: Suppose that Charles Barkley has $25000 to spend on the repair of a gravel driveway. He wants to…

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Q: B) Find all of the second derivatives for f(x, y) = (3xy2 + 2xy + x²) In; x²+y² itable graph and…

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Q: Solve for the given determinant. Use pivotal method until you arrive at a 3x3 where you can use your…

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Q: Locate all relative maxima, relative minima and saddle points (if any) for f(x, y) = (e^x){sin(y)}

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Q: Use the classical fourth-order Runge-Kut initial value problem y' = y, y (0) = 1,

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Q: Q1) Let D = M₂(Z₂)be a ring find the order of D and all the idempotent elements.

A: This is a problem of Abstract Algebra and the Theory of Rings.

Q: Q2: The population of a state is known to grow at a rate proportional to the number of people…

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Q: ch brick is 2" x 8", what is the peri

A: Given that if each brick 2"×8".

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Q: To estimate the population mean, we have seven sample values 8, 10, 2, 7, 5, 13, 4. (1) Find the…

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Q: 2. Find the LU factorization of the following matrices without pivoting 1 2 3 a) A = 2 5 4 354 1 -1…

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Q: Question 3: Consider the following dynamical interaction of giving-up smoking model with constant…

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Q: 7. Trapezoid ABCD has bases AB and CD. If AC and BD intersect at X, then AAXD and ABXC are ?…

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Q: Find the maximum value of f(x, y) = 2x²y³ + 7 on the unit circle. (Give an exact answer. Use…

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Q: nd the vector equation of a line that passes through the point (-2,1,0) and is parallel to the plane…

A: Follow the steps.

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Q: In class, I hinted that normal multiplication (of numbers) is commutative and that matrix…

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