Q2. Let i) ii) f(x)=√√x andg(x) = V1-x Find the domain of the function f(x) and g(x). Compute the formula of the function fogfg.

Q: Q3: Find the solution of the Laplace transforms of the following functions: L-1 ¹ [-35 -3s2-12s-87…

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Q: Rayleigh's equation is y” +4 (½(1¹)² − 1) y′ + y = 0, where µ is a constant. Show that differenti-…

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Q: Paper sheets are required to make a stack of 8cm height. Each paper is 2.5x10-4. How many are…

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Q: What happened to the absolute value of e^-|2t|?

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Q: If f(x) = – 1 1 + 8x f'(x) = Σ – Σ n=1 = Σ (-1)"8"an n=0

A: Follow the steps.

Q: Find the dimension of the splitting field of each of polynomials x+1 and x² - 2.

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Q: T-1 S '(s-2)4 2)4]

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Q: Consider the following optimisation problem min f(x, y) = x + y − x2 subject to x + y ≤ 1 x ≥ 0, y ≥…

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Q: using excel, find the approximation to y(3)= using Euler's method 1st order with h = 0.025, y(2) =…

A: Euler's method uses the formula: y1=y0+hf(x0,y0) to perform the iterations and to approximate the…

Q: The number of bacteria in a container is given by an equation, Q(t)= Qoekt, where t is measured in…

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Q: Evaluate the integral of the given equation below (a) Analytically: (b) Single application of the…

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Q: S Sifoo-gool dx O d2 (f.g) = Sup {/fox) - gox|} V£₁9 € [0₂4] if d, (fig) = Find Ⓒd₁ (√x,x) @d₂…

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Q: (y')2+y'-x=0    solve the differential equation

A: A differential equation is an equation that relates one or more unknown functions and their…

Q: ferential e

A: Given,        y''+11y'+18y=0, y(0)=9, y'(0)=-39

Q: 2. Evaluate: √₁² √2 - x + x da −

A: We know that the modulus function fx=x is defined as x=-x,x<0xx≥0. If we take x=-2, then f-2=2…

Q: The figure below shows a function g(x) and its tangent line at the point B = (2.8, 8.2). If the…

A: The coordinate of point A and point B are given below. A=2.77, 8.14B=2.8, 8.2

Q: Find the highest point, low point and saddle point (if any) of the f(x, y, z)=3x² + 2xy + y²

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Q: Let f(x) = 3x + 2. Use the € – d definition to prove that lim 3x +2 1. x→1 Definition. E-d proof.

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Q: e 1. If F(x) = [ dt, find F(1) and F'(x).

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Q: Let V be R³ and TB = {n₁, n2, n3} and SA = {m₁, m2, m3} be the ordered basis fo 3 2 2 n₁ = - A , n₂…

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Q: Let Xn, Yn be any two sequences. If XnL, YnM, then Xn YnL M

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Q: 3. Let R be the region below bounded by the parabola y = 4 - 2² and the lines 3x - 2y +3=0 and y =…

A: Given the region below bounded by the parabola y=4-x2 and the lines 3x-2y+3=0 and y=0.

Q: A Fourier transform is another integral transform often used in higher mathematics. The Fourier…

A: As per the question we are given the definition of Fourier transform of f(t) as F(ω) Amd from that…

Q: of of H.W: Find and dx dy 1. f(x, y) = (xy-1)² 3. f(x, y) = (x²-1)(y+2) for the functions: 2. f(x,…

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Q: 4. Let T be a tree with n ≥ 1 vertices. (a) Show that T has a vertex of degree 1.

A: As per the policy, we are allowed to answer only one question at a time. So, I am answering the…

Q: Obtain a system of autonomous first-order differential equations in vector field format: (x + y² + x…

A: As per the question we are given a system of second order non-autonomous nonlinear non-homogeneous…

Q: Let (X, d₁) and (Y, d₁) be metric spaces. Let f: X Y be continuous function, then f-¹(G) is open in…

A: Solution

Q: Use the three-point Gauss-Legendre formula to evaluate the integral dx Ső (2x + 1)²

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Q: + Is f one-to-one? is fonto? f:w→ z defined by f(n) = n! = (1) (2) (3)... (n − 1)(n) with 0!: = 1

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Q: Recall the following table, which shows that is a primitive element of the field GF(16)…

A: As per the question we are given a polynomial ring Z2[x] and its quotient ring Z2[x]/(x4+x+1) From…

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Q: The graph of y-f(x) is given below. Which one of the following is the correct equation for f(x)? 70…

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Q: Attachments (n-1)! 69.70.71.....(68+n) If Σ Find the value of x+y.. X y

A: Solution: As we have,  ∑n=0∞n-1!69×70×......68+n=xyRequired to find x+y. Here we use the concept of…

Q: 3 cose and outside r = 3

A: Given: equation of the curve 3-3cosθ & r=3. To find: Volume of region enclosed by given curve.

Q: Question * Every Cauchy sequence in the Euclidean metric space R" with n a positive integer is…

A: True. I have proved using definition of cauchy and convergent sequence.

Q: use cylindrical shells to find the volume of the solid generated when the region enclosed by the…

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Q: Find the following in the form of x + iy 12 1. (1 + i)¹²

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Q: (b) Consider an object of mass m, dropped from some initial height and falling down towards Earth's…

A: According to the guidelines, we will solve first question only.

Q: Chapter 9.4, Question 8 What single payment today would replace a payment of $5000 in one year and…

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Q: Let W be a subspace spanned by the u's, and write y as the sum of a vector in W and a vector…

A: Given vectors are y=466−1, u1=1101, u2=−120−1 and u3=−1011. Now, the formula of orthogonal…

Q: 9. Let f be a continuous real-valued function on (a,b), 8 €R[a, b] with g(x) = 0 for all x E (a. b).…

A: Given- Let f be a continuous real-valued function on a, b, g ∈ Ra, b with gx ≥ 0 for all x ∈ a, b.…

Q: ves the volume of the solid that results when the region is revolved about the y-axis. l (b) Set up…

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Q: 10. Particular solution of y"-4y' + 8y = x³, when x = 0, y = 2, y' = 4

A: We have to find the particular solution of y''-4y'+8y=x3,  when x=0, y=2, y'=4.

Q: 5) USE THE LU FACTORIZATION 20 -3 0 20 - 4 A= b= 1 1 1 02 1 1 -3 4 (COLUMN OPERATIONS) 5 1 2 LAST…

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Q: 3. Let R be the region below bounded by the parabola y = 4 - ²2 and the lines 3x - 2y + 3 = 0 and y…

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Q: (b) Consider an object of mass m, dropped from some initial height and falling down towards Earth's…

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Q: Let C be the curve of intersection of the paraboloid x² + y² = z and the cylinder x² + (y − 1)² = 1.…

A: For the given curve we have the following vector valued function: R⇀=2cost. 1+sint,…