line integral x³ dy), where y is t 3 X counter clockwise.

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Q: 8. (1+e¹¹)² 2

A: Given function is f(t) = 1 + e-t2⇒ f(t) = 1 + e-2t + 2e-t To find linear transformation we use the…

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Q: Q2): A polluted lake has an initial concentration of a bacteria of (1*10' part/m³), while the…

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Q: Evaluate the expression, assume x takes on appropriate range of values sech cosh1 (1)).

A: To Evaluate: sechcosh-14x2Assume x takes on appropriate range of values.

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Q: Mei has taken out a $95,000 mortgage that has an interest rate of 4.7%.  If the loan is for 15…

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Q: Problem : Consider the following van der Pol oscillator: x+µ(x² − 1)x + x = 0 a) Show that the…

A: As per the question we are given a van der Pol oscillator, and we have to find its state space…

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Q: Equations with the Dependent Variable Missing For a second-order differential equation of the form…

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Q: Find the Laplace Transformation of -3x y" +3y + 2y 4e when y (0) = 2, y' (0) = 4 28² +16s+30 OY (s)…

A: Given differential equation: y''+3y'+2y=4e-3x, y0=2 and y'0=4To find: Laplace transform of the…

Q: V. Given: 2. Find f'(2), if it exists. el3r-6-2, f(x)=[2x - 5], √x²-9, if r ≤ 2 if 2 3

A: Given fx=e3x-6-2,if x≤22x-5,if 2<x≤3x2-9,if x>3

Q: Suppose f is continuous everywhere, f’ is differentiable everywhere except at x = -1, and the graph…

A: Here we use the property of symmetrical function.

Q: a+b+c+d=13 2a + 3b-c-1 -3a + 4b + 2c + d = 10 a + 2b + c d = 1

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Q: In 3 Using 4-node Gaussian integration in approximating ³ x ex dx, which f(x) in the formula has…

A: Given: Let us consider the given, ∫1ln 3x ex dx and determine the approximation using 4-node…

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Q: The amount of water, A, in thousands of litres, available in a water tank located on a farm…

A: Given: The amount of water, A, in thousands of litres, available in a water tank located on a farm…

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Q: Find A where R is the region R outside the circle r=2 and inside r= y sin o

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Q: dy y²-x² with = Example 10.16. Using Runge-Kutta method of fourth order, solve y(0) = 1 at x = 0.2,…

A: We can solve this using Runge kutta fourth order method

Q: Use variation of parameters to solve the given system sin 2t x² = (2-1)x - (₂002)¹ X' (4 + Je4t cos…

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Q: Example 9.15. Solve the simultaneous difference equations x+1+v₁₂-3u₁ = x, 3u₁ +vx+15v₁ = 4³ subject…

A: here, u1 = 2 v1 = 0

Q: Find the Fourier Cosine Series of the following periodic function. f(x) = x² 0 < x < 1

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Q: fe²x+Inx² sin x² dx = - +1/√√e²x cos x² dx

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Q: A faire dice is tossed twice -11 LI Pace

A: Given, a fair dice is tossed twice.

Q: Q1): The concentration of salt is given as a function of time by: -=37.5-3.5x dz at the initial time…

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Q: Power Series 2 f(x) = x³ +9x² - 10x + 2 about x = 3

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Q: 10. Prove that 7/2 75/2. sin 0 cos (cos a cosec 8) de 10 T 2 (1-cos a).

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Q: IV. Find Do not simplify your answers. dx 1. cos x + =xcoshy - 2y, where x > 0 cot ¹(x³) sec³ x 2. y…

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Q: Let a = e =es and consider the set U₁8 = {1, a, a²,..., a¹7}. Give the elements of U18 (as powers of…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: Find the derivatives of the function x²(xy² y)² = x² - y² )

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Q: Find the curvature and the radius of curvature at the point t = 0. x = et cos(t), y = e* sin(t), z =…

A: Curvature and radius of converges

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Q: J 2 3 ув-у'-6y=0 y" +2y'= у"+3y"-4y'=0 О

A: According to our guidelines, we are supposed to answer only first three subparts.Kindly repost other…

Q: Identify and draw a sketch of the surface [(x-2)] ^2/9+ [(y-3)] ^2/4- [(z-1)] ^2/36=1 O elliptic…

A: Equation for elliptic hyperboloid of one sheet with center (0,0,0) is  x2a2+y2b2-z2c2=1

Q: . Given the matrix A below, alue for det in A A = 1 0 2 2 0 0 2 1 1 10 1 0 1 4

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Q: Find d(u, v), if u = (2, -4,2,-1,-6) and =(4,-6,2,-1,-6). OA √93-√61 O B. √300 OC √73 OD. V8 O E √32…

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Q: Solve the initial value problem y' = 9y² + xy², y(0) = 1 and determine where the solution attains…

A: Solution of the intial value problem

Q: Let x = [1,1], y = [1,1] € R² and let f: R² ⇒ R² with f(z) = 2₁.x + 22.y for any z = [21, 22] € R².…

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Q: Graetest common divisor of 252 and 664 Greatest common divisor of 252,414,664

A: Greatest common divisors

Q: 2 y (y² - 3x² ) dx + x (3y²-x²) dy = 0

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Q: Ex. (8) Sol Solve [D²-6D+9] y = 54x+18 k

A: Given differential equation is (D2-6D+9)y = 54x+18