1. The function(x)=x-1 has a discontinuity, say where and justify the response. Classify the discontinuity as essential, removable, or infinite. If the discontinuity is removable, rewrite the function so that it is continuous at all reals

Q: Take the Laplace transform of the following initial value problem and solve for Y(s) = L{y(t)}: y" +…

A: please find the attached answer

Q: y"+y=csc²(x)

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Q: Suppose we want to prove: "If n is an even natural number, then for all x € R, x" ≥ 0." Classify…

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Q: A variable plane lx +my+nz = p (where 1, m, n are direction cosines of normal) intersects the…

A: Given: The equation of a variable plane is lx+my+nz=p. (where l,m,n are the direction cosines of…

Q: Given that f(x) = 3x + 1 and g(x) = x2 - 2x - 4, find (g * f)(6). (g * f)(6) =

A: Composite function value

Q: Given that f(x) = 4x + 9 and g(x) = x3, find (f * g)( -2 ). (f * g)( -2 ) =

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Q: Q-1)Find the optimal solution for the Lpp below by using the graphical method ? Max z=X1+X2 S.TO…

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Q: 3-34. The number 6 is represented with + and tiles at right. For each problem below, start with this…

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Q: Apply the Midpoint and Trapezoid Rules to the following integral. Make a table showing the…

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Q: 3. If the continuous random vector (X, Y) with conditional density function Y given X = x is…

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Q: Let A = 61 22 3X=4A + 3B and B = 7 -8-5 1 . Find a matrix X satisfying the given equation. X=…

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Q: sider the discrete-time LTI system -8y[n] + 2y[n 1] + y[n − 2] = −2x[n] + 3x[n − 1]. Find the…

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Q: Question 1 Assume that a sequence (fn)n of integrable functions converges strongly to an integrable…

A: Please find the answer in the next step

Q: Using Equation (11.21), c) Complete the square: c(¹) (∞) = (t) == - i 2 ()* T ia "_H(t)ewor' dt' = +…

A: We have: cb1t=-ih∫-∞tHba't'eiω0t' dt'=-iαh?π∫-∞te-t'/?2 eiω0t' dt'        ........1

Q: (b) Do you think it is possible to change any other numbers in the first three rows of A such that…

A: Please find the attached answer

Q: dx X-Y x+2y

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Q: Consider the u(x, y) = 2x - x³ + 3xy² function. Prove that it is a harmonic function and find its…

A: A function f(x,y) is harmonic is it satisfy fxx+fyy=0. The harmonic conjugate of the function is…

Q: ydx - xdy + 3x²y²e*' dx = 0

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Q: Find all integers n such that o(n) = 40.

A: Use the multiplicative property of ϕ:  if n and m are relatively prime then  ϕ(nm) = ϕ(n)ϕ(m). 40  =…

Q: 2. y+3y"+4y+2y=0; y(0) = 4; y'(0)=-4; y"(0)=1 a. y=e* (4+sin x) b. y=4e¹ cos x c. y=e*(1+3 cos x) d.…

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Q: Find the equation of the line drawn through point (1, 0, 2) to meet the line angles. x+1=2=2+1 at…

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Q: 5. Let A be a subset of 100, that is, A C {0, 1, 2, 3, ..., 98, 99} with cardinality 10. Show that…

A: We shall use the pigeonhole principle which states that if there are n+1 items and only n boxes then…

Q: Let f(x) = 424-82² + 12 Input the interval(s) on which f is increasing. Input the interval(s) on…

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Q: Use Weiestrass's definition of limit to show that lim (7x - 3)= 32. x-5

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Q: 3. Someone selects five arbitrary points in the interior of an equilateral triangle of side 1 cm.…

A: Look at the below image

Q: Use the Laplace transform to solve the given initial-value problem. y" + 3y' = 8(t - 1), y(0) = 0,…

A: Given,       y''+3y'=δt-1,  y(0)=0, y'(0)=1.

Q: The U-Drive Rent-A-Truck company plans to spend $8 million on 280 new vehicles. Each commercial van…

A: Let x be number of commercial vans y be number of small trucks z be number of large trucks Now,…

Q: Let A E R have eigenvalues A₁,..., A. Prove that ker(A-AI)= ker((A-AI)2) for each i = 1,...,k if and…

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Q: answer part ii and iii..... show proper working

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Q: QUESTION 2 a) What is the equation of the straight line that passes through the points (1,-4) and…

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Q: Let 3 denote the centre of a group G. then show that a 3 iff N(a) = G. also show that if G is…

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Q: Part a) Rewrite by peeling off the first term and the last two terms. n+1 k (k+1)! Part b) Rewrite…

A: Given that, ∑k=1n+1k(k+1)!   Consider the first term and last two terms in expansion as follows:…

Q: What matrix would the translate by [1, 2, 3] be? 0 1 0 0 0 0 2 0 0 0 0 3 0 0 0 0 1 0 1 0 0 0 0 1 0 0…

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Q: Problem 4 Find the Fourier coefficients a, and ak of the following waveform X(t)=2t 0<t<1 -2 -1 x(1)…

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Q: So the maximum is (-0.5, -16e^(-1))? And the minimum is (0.5, 16e^(-1))? I need the answer in…

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Q: ABC is a triangle and A = (2, 3, 5), B = (-1, 3, 2) and C = (2, 5, µ). If the median through A is…

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Q: Question 1 Assume that a sequence (fn)n of integrable functions converges strongly to an integrable…

A: please find the attached solution

Q: (b) Let B={(0,2,-2), (1,0,-2)} be a basis for a subspace of R³, and let x = (-1,4,-2) be a vector in…

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Q: Audrey has graduated from college. She wants to rent an apartment for $400 per month. She already…

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Q: Let a plane ax + by + cz + 1 = 0, where a, b and c are parameters, make an angle 60° with the line…

A: ax+by+cz+1=0 →1It makes an angle 60° with the line x=y=z. So we get sin 60° = a+b+c3Σ a2 or…

Q: Solve the matrix equation AX = B for X. A = X= 1-2-3 3 6, B= 6 7 - 1 4 1 -1 -2

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Q: Determine the value of n

A: We know, nC12 = nCn-12 we are given that              nC12 = nC8

Q: x²=-2x+4y y = -4x-2y wh x(0)=2, y(0) = 8 At=01 9+0 2100 JFF Use the Evien Method with a time step of…

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Q: t²y' + 2ty - y³ = 0

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Q: 1. Which of the following sets constitute a subspace of R2? Why or why not? Illustrate each set,…

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Q: . During the class, we derived in detail the first order Richardson extrapolated derivative, by…

A: Note: As you asked only subparts (a) and (b) so, i answered here only (a) and (b).

Q: Consider the following initial value problem. y" + 6y' + 25y = 8(t) + 6(t5a), y(0) = 1, y'(0) = 0…

A: Formula of Laplace transformation…

Q: Question #1: A function is given by f(x) = 6e-3. Now Answer the following: 1. 2. 3. 4. Calculate f'…

A: The central difference formula is given by f'x≈fx+h-fx-h2h (1) For x=0.5. h=0.32…

Q: Verify whether the following sets are subspace of R³/R¹ or not. (i) S = {(x, 2y, 5) : x,y € R} (ii)…

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Q: Evaluate the value (a) sin(2) (b) tan (5) (c) sin-¹(√3/2) (d) sin-¹(sin(¹1))

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