1. Let A = 24 12 -40 20 and consider the linear system = AY. Let Y(t) be the solution 5 What is the long term behavior of this system as t goes to infinity? with Y(0) =

Q: Find the solution to the differential equation below such that y(0) = 14 y' = 10xy - 2x y(x) =

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Consider the initial-value problem y' + ey = f(x), y(0) = 1. Express the solution of the IVP for x>0…

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Q: Find an equation for the level surface of the function through a given point. x-y + 2z (1,0, -1)…

A: Concept: Level surfaces: For a function, w=f(x,y,z):U⊆R3→Rw=f(x,y,z):U⊆R3→R the level surface of…

Q: Identify ALL the Indeterminate forms involved and determine the limit of: limo+ (cos(x))"

A: See the answer below

Q: 10 5(5+10) a/n A ナ B 5+10

A: See the details solution in below

Q: 4. How many solutions are there between the plane P₁: (x, y, z) = (4, −3,−1) + s(1, -3,1) + t(2,4,…

A: Plane and line

Q: The differential equation y""+ay""+by" + cy + dy = 0 6t has a solution y 2tet 6e sin(3t) for real…

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Q: ART 1 Differentiate the following items below by completing the table. Copy the table and write your…

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Q: lim f(x) = 9 lim_ g(x) lim_h(x) = 0, X→2 X→2 X→2 find the limits, if they exist. (If an answer does…

A: Topic = Limits

Q: Let E be the region in the first octant enclosed by z = √√√x² + y² and z = 2. Which of the following…

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Q: 3. Consider the vectors X and Y in R³ where X = -i+3j and Y = 4i-2j+ 2k. 1, Find the unit vector…

A: We can solve this as follows:

Q: Find the general solution of the given differential equation, and use it to determine how solutions…

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Q: 3- Find the area between the parabola x² = 4y and the straight line x-2y + 4 = 0

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Q: Identify and sketch the graph of y = x² + 1 in R³.

A: Given:

Q: Evaluate: limt o sin 3t t5 (t-1)² using L'Hôpital's

A: Since you have asked multiple questions in a single request we would be answering only the first…

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Q: Given a function, Based on the function, 2s +3 F(s) = s² -2s+25 a) Determine f(t). b) Based on…

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Q: E S™ SX 5x5x²x² coscyl dyd z d x "X d 2 +

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Q: 2. 2y² SS dxdy 1 y

A: Disclaimer: Since you asked multiple question,we will solve the second question for you. if you want…

Q: Instruction: Evaluate the following Integrals. Write your COMPLETE solutions neatly and organized.…

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Q: If c is a constant, what is the limit of c as x approaches a? 0 C a X

A: A detailed solution is given below.

Q: Using the laplace transformation table, evaluate the following, considering any other variable other…

A: A detailed solution is given below.

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Q: 10 Let u= (1, 2, -1) and v= (3,-1,2) be two vectors in Rª. Which of the following is a normal vector…

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Q: 10. Prove that any cyclic group is abelian.

A: As you are asked multiple questions but as per our guideline we can solve only one. Please repost…

Q: xcsc {( 2 ) - »]dx + y y dx+xdy=0 X (x² − xy + y²)dx−xydy=0

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A: John invested his inheritance of $12,000 in three different funds: part in a money-market fund…

Q: Let A be a 2 x 3 matrix, B be a 2 x 3 and C be a 2 x 1 matrix. Which of the following could be ABC?…

A: follow next step

Q: 41- - ST x² coscyldy dz dx

A: ∫ cos(y) dy= sin(y)+C

Q: Find the solution of the given initial value problem. π ty' + 2y = sint, y "(-) = 5, t > 0 Y ||

A: Concept: linear differential equation of the form dydx+Py=Q The general solution of the linear…

Q: Solve the problem using implicit partial differentiation. Show your complete solution. No shortcuts.…

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Q: Write an equation describing the relationship of the given variables. y varies inversely as the cube…

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Q: 22 Given the cross product of 2 vectors u and vis, u x v= -3i-3j+3k, and their dot product is,…

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Q: What is S (x² + 2x)² dx? + x³ + ³x² + C 4 S (x² + 2x)²dx = ¹x¹ + x³ + 4 f (x² + 2x)²dx = (x² + 2x)¹…

A: We know, ∫xndx= xn+1/(n+1)

Q: L’Hopital

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Q: Which one of the following is the domain D for f(x, y) = ln (2²-(y-2)²) ? Select one alternative:…

A: The given function: fx,y=lnx2-y-22.We need to find the domain.

Q: x-2x +x= 15; x (0) = 7, x (0) = -16 hand written plz

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Q: -2 2 о 0 Ау N Х

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Q: Given the equation z = arctan(x- y²) with the change of variables x=s³-t³ and y=st² + s²t, use the…

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Q: x -2x +x= 15; x (0) = 7, x (0) = -16

A: This question is based on diffrential equation solved using Laplace transform.

Q: Given the table of values of the function below, what is its limit as x approaches -1? x -1.25…

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Q: How. Find the lengths for the following curver. 7 \- r = 1 + cosa

A: I am attaching image so that you understand each and every step.

Q: Determine whether the differential equation (4x² − 2xy + 6) dx + (2y² − x² + 4) dy = 0 is exact. If…

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Q: f(x) = 2²3 on (0, ∞) x+3

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Q: 2 ln x + ln (x+1)- 1/2ln (x^2+1). Compress the logarithmic expression.  PRE-CALCULUS HW question..…

A: The given expression,   2 lnx+lnx+1-12lnx2+1

Q: Find the integrating factor by inspection then solve the following differential equation. Show your…

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Q: - Find the area between the parabola x² = 4y and the straight line x-2y + 4 = 0

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Q: Find the limo (cos x) = Show your complete solutions. No shortcuts.

A: Given,  limx→0cos x1x2

Q: Identify and sketch the graph of y = r²+1 in R³.

A: