[E] Four subject teachers Ali (A), Diana (D), Georgina (G)

Q: Consider the function defned by fCX, y) - y-ex (a) Find the domain and ran ge of f. (b) Draw a conto…

A: Given data  f is a function x&y  f(x,y)=y-ex  (a) find the domain and range of f=? (b) draw a…

Q: Consider thie integral | lizl + z dz (a) Compute the above integral when I is the circle |2| = 2,…

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Q: 4 1. xln?x 00 8

A: To find the convergence of integral we consider the corresponding indefinite integral and evaluate.

Q: Consider the product of cycles (1 2)(4 7 8)(2 1)(7 2 8 1 5) that are permutations of {1, 2, 3, 4, 5,…

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Q: 3. Find the arc length traced out by the endpoint of the vector-valued function 1 †(t) = t cos t î +…

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Q: Let u, = 5" cos" xcos nx dx. It turns out that u,u, u,. form a GP. Find %3D (a) the ratio of the GP.…

A: We need to find value of un fir different values of n and then find series representing u1 , u2 , u3…

Q: Let R be a ring such that for each a e R there exists XE R such that ax = a. Prove the following :…

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Q: Exercise 2 Let 1 B = 3 C = These are bases for R? (no need to prove this). Find the change of…

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Q: 6- Use Newton-Raphson method to solve the system x3 +y – 1 = 0 y3 – x + 1 = 0 with the starting…

A: f1=x3+y-1=0→(1)f2=y3-x+1=0→(2)(x0, y0)=(1, 0) Formula for Newton-Raphson…

Q: Definition: The area A of the region S that lies under the graph of the continuous function f is the…

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Q: 3. If the radius of the circle were 2, would that change the value of the sin, cos, tangent for each…

A: Let us write the reasons of the circle based problem in the next step.

Q: ) Find the transition matrix from the ordered basis of R? to the ordered basis of R².

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Q: Use the method of disks/rings to determine the volume of the solid obtained by rotating the triangle…

A: To find the volume of a solid obtained by rotating a region (bounded by two curves) about a line,…

Q: У" - бу + 5у %3DЗе *; у (0) — 2; у'(0) — 3

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Q: 6. 'The mapping T :R³ → R? is defined as T (x, y, z) = (x + 2y+ 3z, x + 3y + 2z) is a linear…

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Q: d. ý <(1+s)y, ,h=o•2 yCi) = e

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Q: Let a +b = 4, where a 0 for all x, prove that g(x) dr + g(x) dx increases as (b- a) increases.

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Q: Solve using Gaussian Elimination with back-substitution or Gauss Jordan 0.02z1 - 0.05z2 = -0.19…

A: Consider the given system of equations, 0.02x1-0.05x2=-0.190.03x1+0.04x2=0.52 So, the matrix form of…

Q: 4) Find the volume of the solid under the surface z = x3 and above the plane region bounded by x =…

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Q: Use the Euler, improved Euler and Runge-kutta methods to solve the following ODES: y co) = し h=o.2…

A: Given the ODE y'+5x4y2=0 and  y0=1⇒x0=0, y0=1   Step size h=0.2 Solve using Euler's Method at a…

Q: Determine whether or not the following statement is true: If A and B are 2 x 2 matrices, then (A+B)²…

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Q: Exercise 2.5.1 Suppose T : R" + R" is a linear transformation. Prove that T is an isometry if and…

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Q: Buien : 0 =y2 + xy A = yi t2j +(421x) k %3D %3D

A: # as per the guidelines we are entitled to solve one question at a time ,please resubmit the other…

Q: Hew. O find the root of PW=R-1)e_1 sush that I f cast < Ix 65 , we NiP.M.

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Q: What is the surface area? 4 in 3 in 2 in square inches

A: We know, surface area of cuboid= 2(lb+bh+lh) unit2 Where, l= length              b = breadth…

Q: A line passes through the points P(9,5, – 1) and Q(- 9, – 3, – 8). Find the standard parametric…

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Q: Let U be a universal set and A, B, C CU. ITEM 1. Prove: A n BCAUB

A: # as per the guidelines we are entitled to solve one question at a time please resubmit the other…

Q: 4) Using Rational Root Theorem and Descartes' Rule of signs. Find all roots of f(x)= x° + 8. What…

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Q: You spin the spinner, flip a coin, then spin the spinner again. Find the probability of the compound…

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Q: Find the particular solution to the equation - 5t ]n t y'' + 10y' + 25y = e Yp(t) =

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Q: Use Ring Method Rotate the region bounded by y = x2 – 2x + 4 and y = x + 14 about the x – axis.

A: The given curves are y=x2-2x+4 , y=x+14 and x -axis To find: the volume the region bounded by the…

Q: 6. (a) Express the function f(x) = x in on [0, T] as a Fourier cosine series S(x). What is S(-1)?

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Q: The value of the triple integral 22 zdV where E is the upper E half of the sphere of x² + y? + z? =…

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Q: Prove that L(f) ≤ 0 ≤ U(f). Given that the bounded function f : [a, b] → R has the property that…

A: Given that the bounded function f : [a, b] → R has the property that f(x) = 0 for all x ∈ [a, b] ∩…

Q: f If f(x, y) = y cos(x) – x³ In(y), find the second partial derivative dy dx

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Q: Use the method of disks/rings to determine the volume of the solid obtained by rotating the triangle…

A: given vertices of a triangle 3,2 , 7,2 , 7,14 use method of disks to determine the volume of solid…

Q: Which of the following is not linear in the variable x and y? O 2x-3y =4 %3D O a? + y? = 4 %3D +2…

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Q: 21. lim x2 – 2x – 8 = 6 - - x 4 x – 4 -

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Q: 5. Consider the nonlinear system. Sx = -2y + xy = x + 4xy (a) Find all the equilibrium points of the…

A: Given non-linear system is x'=-2y+xyy'=x+4xy for equilibrium points -2y+xy=0x+4xy=0 which can be…

Q: r) suppre z is a function of xX and y, and asc Jee+yz: 2Y evinx for dz Solve and dz

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Q: 5. (i) Let A be an nxn matrix over C. Show that the eigenvectors corresponding to distinct…

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Q: SEGMENT Directions: Solve for x. Clrcles may not be drawn to scale. I. 2. 4 6. 3 5. 4 3.

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Q: Solve the initial value problem (3+x*)y" + 4y = 0, y(0) = 0, y(0) = 12. If the solution is y = co +…

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Q: 1. 2– 2y + 2z = 3r – 2y + 2z = 3 2x – 3y – z = –72x – 3y – z = - 7 -x + 3y – 3z = –4-x+ 3y – 3z = –…

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Q: 3" + 27+1 (c) Evaluate 5" n=1

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Q: dY Consider the linear system: dt Y. (a) Show that the two functions Y1(t) = () and Y2(t) : 2t) are…

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Q: The size of an unborn fetus of a certain species depends on its age. Data for Head circumference (H)…

A: Given that H = -30.98 + 1.822t2-0.9193t2log(t). Where t is age in week.

Q: . Let a be any non – zero vector in V and let p. be the T – annihilator of a. (i) The degree of pa…

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Q: Q2: Find a root of x- 0.5 – 2-2x = 0 by using Newton-Raphson method correct to %3D 4 decimals so…

A: x-0.5-2-2x=0⇒f(x)=x-0.5-122x⇒f'(x)=1+2ln(2)22x Taking initial guess x0=0 Newton-Raphson method:…

Q: 16. lim (2 – 3x) = –4 x 2 %3D

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