Consider the matrix (a) Find the eigenvalues of A.

Q: 2. Verify the final value theorem for the function 3t²e¬4t and determine its steady state value.

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Q: Find the general solution of this ODE: d²y dy + 7. + 10y = 3t2 + 4t – 1 dt? dt

A: We have to solve the given differential equation.

Q: What is the particular solution to the differential equation +1+y = 2e- with y = 1, 2=-1 when x = 0?…

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Q: Consider A = (0,4, 2) , B =, (6, –1,0) and C = (3,0, 1). (a) Find the unit vector having the same…

A: given vectors A=0, 4, 2, B=6, -1, 0, C=3, 0, 1

Q: Which of the following is the general solution to the differential equation (3 + 8y³e(3y=x))dy – dx…

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Q: expansion of valid in )(z-2) ient of is

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Q: 36 for 0 <= u <= 6 and 0 <= v <= 2(pi) where <= is less then equal too where pi = 3.1415

A: Introduction: An ellipse is the locus of all points that satisfy the equations.x = a sint,  y = b…

Q: Find a basis among the vectors [1,1, 3]; [–1,0, 10]; [0, –3, –2]; [–1, –3, –5] (which are surely…

A: Here we are given 4 vectors in ℝ3, which are:1, 1, 3; [-1, 0, 10]; [0, -3, -2] and [-1, -3, -5]To…

Q: The temperature in a room changes at a rate of r(t) = In(t + 1) sin(t) degrees Celsius per ho tis…

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Q: (d) If v is an eigenvector for a matrix A and a matrix B then v is an eigenvector for A+ B.

A: TrueJustification:Suppose v is an eigenvector for a matrix A and a matrix B.Then there exist real…

Q: exercise Find the laplace of each f(t) 1. 5sin2t – 6cos2t

A: Since you have posted a multiple  question according to guildlines I will solve first   question…

Q: Use X = X + X, = eAtC + eAt e-As F(s) ds to find the general solution of the given system. Jto 10 X'…

A: Given x'=1004x+te6t

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Q: xy Let f (x,y) =In Then f „(1,- 1) =.. %3D 3x2+4y3 XX

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Q: 00 x" „n +1 If the series > has the radius of 5, then the radius of convergence of the a n+1 n=1 00…

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Q: Consider the IVP: x" + x = 4e ; x(0) = 1, x'(0) = 3. Find the general solution. A x(t) = 2e'+cost –…

A: Given differential equation is x'' + x = 4et ; x(0) = 1, x'(0) = 3

Q: 3. Give the parametric and symmetric equations of the line that passes through the point (4,-3,5)…

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Q: Consider the IVP: y" + 9y = 40ex ; y(0) = 5, y'(0) = -2. Find the general solution.

A: Use the given differential and initial conditions.

Q: Evaluate the integral shown using Simpson's 1/3 Rule with 20 panels. 12 4arctan dx O 32.52059525 O…

A: Given integral is ∫2124arctanx6dx

Q: Relationship Y= (ax+bX) - Find the Linearizationof Nonlinear

A: This is the problem of application of differentiation.

Q: 1 Find the Inverse Laplace Transform of s2+2s+ 10 (A -e "cos3t 3 1 B -e -'sin9t 3 3r -e"cost D -e…

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Q: 1. Consider A = (0, 4, 2) , B =, (6, –1, 0) and C = (3,0, 1). (a) Find the unit vector having the…

A: Given,A=0,4,2, B=6,-1,0, C=3,0,1To find: a) Unit vector              b) Sketch of the unit vector…

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Q: prove that - Every groupof order y i's cyclie.

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Q: Evaluate the line integral. e ds where C is the curve given by x=2t, y=3t, 0<t<2

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Q: Find the Inverse Laplace Transform of (s+4)3 A ³(2cos21 + - sin2t) e-2(cos21+ -sin2t) (2cos21 +…

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Q: Calculate the work done by the field F when the object moves along the given path from the initial…

A: To find Work done by the field F when the object moves along the given path.

Q: (1+t2) ds + 2t[st2 – 3 (1+12) ²]dt = 0; when t = 0, s = 2.

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Q: Determine the general equation of the plane containing the points P(1, -4, -5), 3 Q(2,0, 13) andR

A: We have to determined the general solution of the plane that containing the points P(1, -4, -5),…

Q: Find an isomorphism from the group G = to the multiplicative group {1, i, – 1, – i} in Example 3 of…

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Q: Find the solution. dy y dx A y = 8 8 (B y = 4 y-2 8 (D y = 8.

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Q: Question 17 Find the solution. (4D3 + 4D2 + D)y = 0 A y = c,x+ (e,+cz)e¯/½ B y = c e © y = c,+…

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Q: If (a,b) denotes an arbitrary interval of numbers on the real number line, Find the probability when…

A: Given [a, b] an arbitrary interval of real numbers.

Q: Let! aset os R, sho that whe ther Tbe acofinite to pology on (R,T) is To-spuce and TisPuceand or not…

A: The given question is related with topology. Given that Τ is the co-finite topology on R . We have…

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Q: Let f (x) = e4x. Find p3(2), the value at x = 2 of the third Taylor polynomial about 0, and r3(2),…

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Q: (1 – x)y" + y = 0, y(0) = 6, y'(0) = 12

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Q: The 3 x 3 matrices A and B are defined in terms of a scalar constant k by [k 9 A = 1 k l5 -1 a. Find…

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Q: Consider the following IVP: y' +y = e2t ; y(0) = 0 Find the general solution. 1 -211 A у () 3 21 B)…

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Q: Consider the following IVP: y"-3y'+2y = e3t; y(0) = 0, y'(0) = 0 Find the general solution. A y(t) e…

A: Given differential equation is y'' - 3y' + 2y = e3t ; y(0) = 0, y'(0) = 0

Q: 2. Integrating factors found by inspection.: y(x² – y² +1}dx-x(x² – y² –1}dy = o

A: We have to solve the given differential equation.

Q: Show that the lines L:a =4- t, y = 2t, z =1+t and L2:2 =1+ 21, y = 3 – 4t, z = 5 – 2t are parallel…

A: This is a problem of 3D analytical geometry and application of calculus, vector calculus.

Q: Express the following permutation as a product of disjoint cycles. ). 1 2 3 4 5 6 7 8 9 10 11 12 f 2…

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Q: [2 - 3 11 c) Let A = |1 2-3 and be express as A = LU as below L4 2 01 1 3 U13 2 1 U23 [41 0 [2 – 3…

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Q: 2s + 3 Find the Inverse Laplace Transform of (s+4)3 A e"(2cos2t +- sin2t) 2 (cos2t+ -sin21) (2cos21+…

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Q: 5. Identify and sketch the graph of the following equations in R. (a) a2 + 2y? + 2² - 8r + 12y – 2z…

A: (a) The given graph is a sphere. This graph does not pass through the XY plane, YZ plane and the XZ…

Q: ind the Laplace Transform of f(t) = cos² 3t A F(s) = 2 s2+36 B F(s) = + s2+36 6 F (s) = + s²+36 2 s2…

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Q: Kora uses the following ingredients to make 1 s'more. Ingredient Amount Graham crackers Chocolate…

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Q: What is the particular solution to the differential equation dx 1 + y = 2e-* with y = 1, dy -1 when…

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