Use the method of variation of parameters to solve the initial value problem x' = Ax + f(t), x(a) = x₂ using the following values. [:] A = x(t) = 4 - 17 1 -4 f(t) = 8t 4 , x(0) = At cost + 4 sint sint - 17 sin t cost-4 sint ...

Q: 2. Letf: R→R be defined by f(x) = 4x -x2. Let B be the range of f. (a) Find B. (b) Fins f-1([0, ∞…

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Q: Solve the system of equations by any method. 5x +9y = 15 x 2y = 4 Enter the exact answer as an…

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A: Let's solve given integration.

Q: 3. Use polar coordinates to evaluate the double integral. (a) ff sin(x² + y²) d4, where R is the…

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Q: \(\) The geometric representation of the equation -4x² - 4y² = -12 is not a cylinder in R².

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Q: =3. Let a = [2₁1,-1], 5o = [4₁-5, 3] and C-[-1,-2,5]. compute ax (b + c). Show full steps.

A: We have to solve given Questions.

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Q: Estimate the slope (slope = rise/run) of the tangent line to the curve. Ау 10- 9- 8 7 6 5 4 4 -1 0 I…

A: Here is the solution.

Q: 16. If g(x) = x + 2 cos x, then the equation of the tangent line to the graph of g at x = is 3π 2 A.…

A: This is a basic application of derivative problem

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A: The 5 points are the following.

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Q: a. Write the equation of the line that represents the linear approximation to the following function…

A: Using linear approximation at x=a L(x) ≈f(a) + f'(a)(x-a)

Q: 1- Let n and r be positive integers such that r≤n. Then (a) Pn=nx pn-1 (c) P = pn n-1 (b) P = P-1…

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Q: at L'Hôpital's rule may not apply or may require multipl w and, if necessary, fill in the answer box…

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Q: Evaluate the following double integral by converting to polar coordinates where J 5xy 2x² + 2y² R…

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Q: 2. Find the first 4 terms of Taylor series for the function (In x4) about x = 3 ?

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Q: B: Solve the following integrations: fx³e-2x¹ dx b-S. -dx x³ +10 c-f 3sec³x. tanx dx arks

A: a) ∫x3e-2x4dx Let x4=t Then, 4x3dx=dtOr, x3dx=dt4 By substitution,…

Q: SUBJECT: DIFFERENTIAL EQUATION TOPICS Growth/Decay  Newton's Law of Cooling/Heating Mixture Simple…

A: Given that, A tank has pure water flowing into it at 10 liters/min. The contents of the tank are…

Q: Cursive

A: Please refer to the image below

Q: @)X = y² + 1₁ x = 0, y = -1 y = 2 The appropriate integrand to find the volume of the solid…

A: Solution is given below:

Q: дz If x² sin(2y - 5z) = 1 + y cos(6zx) defines z implicitly as a function of x and y, find [Show…

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Q: 6. Let A= (1, 2, 0), B = (3, 4, -1), and C= (4, 5, 2). Find the exact value of the distance between…

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Q: Q4\A: Find area of zone bounded by curves y = x² y = 2x+8

A: area bounded by curve  y = x2  y = 2x +8  step 1  find the intersecting point of curves step 2  find…

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A: A Sequence is said to be convergent if it approaches some limit. A sequence is said to be divergent…

Q: 2 1 Lotes So I+ y² xyer² 0 1+ 0 Evaluate Select one: ○ In 2 O ln 2 O 1/4 ○ In 2 O 1/2 O 1 -dydx.…

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Q: The vectors a (4, -10,8) is perpendicular to the vector b (8,-8, -14). Select one: True False

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Q: Use the properties of limits to help decide whether the limit exists. If the limit exists, find its…

A: We have to check whether limit exists or not  And if exists then what is the value of the limit

Q: 63. 100% los telborey adi The graph of g consists of a semicircle and two line segments for -4 ≤ x ≤…

A: To find the area between the given curves.

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Q: The approximated value of the integral fe* dx is equal to - Rule with step size (h=2). when using…

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Q: ا 1 x2(x – 1) dx

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Q: why do you think is important to calculate those 8 basic ratios  shown in picture

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Q: For x = - 5, determine whether f is continuous from the right, from the left, or neither. (graph…

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Q: 5. The sequence of partial sums of the equation Σ (a)3/2 (b) 3/4 n=1 3n-1 (c) 1/3 (d) -1/3

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Q: In problems 1 and 2, list both the order of the DE and state whether the DE is linear of nonlinear.…

A: Given question:- In problems 1 and 2. List both the order of the DE and state whether the DE is…

Q: let (5,-7) be a point on the terminal side of 0

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Q: 63. ei (x) gouloeteluoisey aut Ho The graph of g consists of a semicircle and two line segments for…

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Q: Q3: A: Solve the following differential equation Ỳ – (sinx) y = 2 sinx

A: We can solve the given differential equation by using the variable separable method.

Q: Let f(x) = 5x² - 4 to find the following value. f(t+1) f(t+1)= 5t+10t+1

A: Given f(x)= 5x2-4

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Q: Find the vertical asymptotes of the function. y = 2x² +1 3x-2x²

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Q: Q ssosiee ※ dy nolaeV DOY MEMedua s x24

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Q: Compute the definite integral π/4 0 5 sin² (3x) dx

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Q: Consider vectors A-40+30) and B-4.02 +8.03. ▾ Part C If the direction (but not the magnitude) of B…

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Q: Solve using Inverse Operaators. y"" - y' = 4e-x + 3e2x; x = 0, y = 0, y = -1, y = 2 Particular…

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Q: buty What are all values of x for which the function f defined by f(x) = (x² - 3)e-* is increasing?…

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Q: III. Evaluate the given definite integral: ₁*√x edx

A: ∫14 xexdx here we have to integrate using substitute method  so for that lets substitute x = v dv/dx…

Q: 3. Solve Trigonometric Equation (a) 1+ sin 8 = 2 cos²0 (b) cos 0 + 1 = sin 0,0 € [0,2π) (c) √2 sin…

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Q: In Exercises 101-108, assume that each sequence converges and find its limit. 101. a₁ = 2, an+1 102.…

A: The objective of the question is determine the limit of the given sequence.

Q: Solve 23x. 77 5x 4.2

A: Here the given problem is,              23x=4×25x We need to find the value of x.