"Determine the area of the triangle in R2 with vertices: (−1, 4),(3, 2),(0, 1)."

Q: Q. Y prove that a) X (o) H Lim X(Z) Z→∞ b.) x (∞0) = Lim (Z-1) X (Z) Z-1

A: a) To prove that x(0) = lim(z -> ∞) x(z), you can use the definition of the limit:lim(z -> ∞)…

Q: 5. Given two Cauchy sequences {an}_1, {bn}_1 in Q. Show that (a) {an + bn}_1 is Cauchy; (b) (anbn)…

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Q: find the general solution by finding the homogeneous solution and a particular solution.   1) y" +…

A: Given information:The differential equation: To find:The general solution by finding the homogeneous…

Q: The graph of a function is shown on the coordinate plane below. Identify the rate of change of the…

A: The rate of change of a function is the slope of the graph of the equation at a given point on the…

Q: Find the limit e(-y)³-1 lim (x,y)-(3,3) (x - y)²

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Q: The fission reactor of a nuclear plant explodes at t = 0. The following function d represents the…

A: (a)This method is useful for obtaining an approximate response, but it cannot provide an absolute…

Q: (a) A signal applied to a servomechanism system is defined by the function as, 0 4 5 f(t) = 2t+1 9…

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Q: The function y₁ = x². ln(x) is a solution to the DE, x²y"-3xy' +4y=0. Use the reduction of order…

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Q: Q2:- Are the following function analytic? f(z)=Re(z²)-ilm(z²)

A: Given: We have to check that the given function is analytic or not.

Q: A tank is filled with a fluid with density 54 The cross-section of the end of the tank is given by…

A: The slice is shown below:The volume of slice is,

Q: 7. Determine the values of k for which the following quadratic equations x²+kx+9=0 with have: a. One…

A: Given quadratic equation: We have to determine the values of  for which the given quadratic equation…

Q: 2 1 0 -1 -2 -3 -4 3 F(x, y) = 4x + 4y²j F(x, y) = 4y²i + 4xj F(x, y) = 4yi + 4x²j F(x, y) = 4x²i +…

A: We have to identify the vector field

Q: 1. f(x) = x² 9 2. f(0) = cos(30) g(x) = 4|x|² 3. f(t) = et cos(ut) 4. f(x) = e³x 9 9 9 g(0) = 12…

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Q: of V = R¹X3. Find a matrix X E V such that Un W = span{X}. =[ X

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Q: Can you only use matrix, not wronskian. Also indicate what method of matrix was used.

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Q: 4. Let A1 -2 1 -3 2 (1) Find the eigenvalues of matrix A and the corresponding eigenvectors. (2)…

A: Given information:The matrix .To find:(1) The eigenvalues of the matrix and the corresponding…

Q: me table below shows the production of tobacco in the US, in millions of pounds.¹ Year Year 2006…

A: (a) The average rate of change in tobacco production between 2008 and 2019 ismillions of pounds per…

Q: Let f(x) := x² for x∊R, and let E := {x∊R : -1≤x≤0} and F := {x∊R : 0≤x≤1}. Find the sets E\F and…

A: Given, f(x) := x² for x∊ R,  E := {x∊ R : -1≤x≤0} and F := {x∊ R : 0≤x≤1}.

Q: The set B={1-1²,1-1², 1+2t-12) is a basis for P₂. Find the coordinate vector of p(t) = -1+6t-3t²…

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Q: 3 The linear function p(x) has a slope of - and passes through the ordered pairs (0, 3) and (-5, 0).…

A: The linear function p(x) has slope  and passes through the ordered pairs The exponential function…

Q: The goods and services tax​ (GST) is a federal tax charged on the cost of almost all goods and…

A: Solution:- From the given date ,We have to find how much GST must Fred send to the government,Now…

Q: Hello there, I don't understand the writing for problem 2. Can someone write the solution neatly?

A: We have to find here, D'Alembert's ratio test:If , then the series diverges and i.e., a limit does…

Q: Q1:- Calculate sin(π/4+i)

A: Results:

Q: MATHMATICS For each of the following subsets of the integers ℤ, explain whether the subset is…

A: Given sets are : i) The set of even numbers in Z ii)  The set of perfect squares in Z iii) The set…

Q: 25. Vector A points in the positive x direction and has a magnitude of 75 m. The vector C = A + B…

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Q: 3. 4. For the function y = A sin(B(x − C′) ) – D, which variable determines amplitude? A b. B C. с…

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Q: Question 1. Show that the limit does not exist. x³y² lim (z,y) (0,0) 24+y8

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Q: Suppose you want to have $700,000 for retirement in 35 years. Your account earns 7% interest. How…

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Q: find the general solution by finding the homogeneous solution and a particular solution. 1)…

A: Given differential equation: We have to find the general solution of the given differential…

Q: A system of two 3000 L holding tanks is set up with a pipe bringing water to the first tank, another…

A: As per the question, there are two L holding tanks with water flow and salt dissolution.Our…

Q: Orthocentre and circumcentre of triangle ABC are (a, b) and (c, d), respectively. If the coordinates…

A: Given that the orthocentre H(a,b) and the circumcentre O(c,d).Since relation between H, O and G…

Q: In Exercises 15-20, W is a subspace of R4 consisting of vectors of the form X = XI X2 X3 X4…

A: As per our company guidelines we are advised to solve only the first question. Kindly repost the…

Q: K -(x-y-1) dy

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Q: Find the maximum value of f(x,y) = 31-x² - y² on the line x + 5y = 26.

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Q: The parametric equations and parameter interval for the motion of a particle in the xy-plane are…

A: The parametric equations and parameter interval for the motion of a particle in the xy-plane are We…

Q: 4. For u, v, and w in Exercise 2, find nonzero scalars C1, C2, C3 such that c₁u + c₂v + c3w = 0. Are…

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Q: 2. Consider matrices of the form -2 1 = a ( - 1² - ²2² ) + ³ ( -7 _ ²2 ) B B -2 1 -2 (a) Ma,B≥ 0.…

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Q: Consider the subspaces U = span{[4 0 1],[4_1 −4]} W = span { [-5 3 3], [-5 3],[−5 4 −2]}

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Q: 3. 4. Consider the matrix A = 3 0 0 3 1 1 2 23 (1) Compute the determinant of A, i.e., det(A) and…

A: Given, So, matrix A is nonsingular.

Q: A ferris wheel is 10 meters in diameter and boarded from a platform that is 2 meters above the…

A: From the given information, we have to find the amplitude, midline, period, and your height after 1…

Q: Solve for the exact first order differential equation. Find the appropriate integrating factor and…

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Q: Find approximate values for f' (x) at each of the x-values given in the following table. Use a…

A: For right hand approximation x2>x1For left hands approximation >x1>x2

Q: Let U = {1, 2, 3, 4, 5, 6, 7}, A={2, 3, 6, 7}, and B = {3, 5, 6}. Find the set A¹ n B'. A' B'= (Use…

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Q: If A(-2, 1), B(2, 3) and C(-2, -4) are three points, find the angle between BA and BC.

A: Given points are A(-2,1) , B(2,3) and C(-2,-4).We have to find the angle between the lines BA and…

Q: The graph of a function h (x) is shown to the right. Which of the following conclusions can be made…

A: Given

Q: Consider f(t) = -5t+9√t Determine the intervals on which f is decreasing. Of is decreasing on: Of is…

A: The given function .The aim is to find the increasing and decreasing intervals and the local…

Q: 1. Show that the following functions are convex by verifying the definition, i.e., that f(x + (1…

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Q: Find the linear approximation of the function f(x) = √25-x at a = 0 and use it to approximate the…

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Q: 16. Let V and W be vector spaces such that dim(V) dim(W), and let T: V → W be linear. Show that…

A: Answer (A),Let V and W be vector spaces such that dim(V) = dim(W) and let  be linear.Now, we need to…

Q: t-14 t-7 Determine the intervals on which g is decreasing. Consider g(t) = Og is decreasing on: Og…

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