Solve the equation using Reduction of Order (D² - 5D + 6) y = 2e* Oy=e+c₁e²x + 2c₂e³x Oy = √² + ₁³x + c₂e²x

Q: Find the length of the arc of a circle of diameter 8 meters sub tended by a central angle 2pi/3…

A: Let "θ" be a central angle in a circle of radius "r". Let "s" be the length of the arc cut off by…

Q: 6.) Find the local extrema and saddle point(s) of f(x, y) = x²y-6y²-3x².

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Q: Find the position vector for the vector v, whose initial point is (0, −2) and terminal point is (5,…

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Q: Calculate the volume of solid of revolution when the region bounded by y = √x - 2 and x-3y - 2 = 0…

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Q: drug is administrated intravenously of the object iver 1. the time interval [3,8] Use definition of…

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Q: dy dx +y = 0 y(0) = 1 Using Power Series, solve for y(x) at x₁ = 0 Using First Order Runge-Kutta…

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Q: Evaluate the following integrals: 1. f (cosx- sin x) dx 2. fcot²x dx 3. f (sin x + x) dx

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Q: 1 to 21. Use the Cauchy-Riemann conditions to find out whether the functions in Problems 1.1 to 1.21…

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Q: (d) √ ² (3 (3 − z)(3z + 1) dz. 0

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Q: Differentiate and simplify this function k (t) = e√t^2+t+1 - e-√t^2+t+1

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Q: Which of the following gives the volume of the solid created by revolving a curve f(x) around the y-…

A: We need to choose correct option.

Q: Determine the equation of the ellipse with foci (1, 4) and (-5, 4), and co-vertices (-2,8) and…

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Q: Using Ratio Test the following series +∞ (n!)² Σ 3n n=1

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Q: Evaluate the integral. (Use C for the constant of integration.) [(sec²(t) i + t(t² + 1)² ₁ + t²…

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Q: Q3. Determine whether the function is continuous at x=1 or not (x² - 1 x = 1 f(x)=x-1 2, x = 1

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Q: What is the equation of the given ellipse? Y (-3, 2) (-1,-1.5) X

A: Graph of the ellipse is given, we have to find its equation.

Q: Solve the following first order differential equations, clearly showing all calculation steps dy…

A: Given that differential equations and we find the solution of this differential equations by using…

Q: Calculate the area and show the graph of the curves:

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Q: For the given double integral, sketch the region of integration and write an equivalent double…

A: Given problem:-

Q: 2 Evaluate r sin rdr using integration by parts.

A: Given∫ xsinxdx

Q: The function f(x) = 7 1+9x² f(x) = 2 chan Σar n=0 Find the first few coefficients in the power…

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Q: 2. Find the Maclaurin series of f(x) = tanh ¹x

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Q: 1. A force vector has a magnitude of 23 N and makes an angle of 35° with the x-axis. What is the…

A: We know that, vertical component = y-axis

Q: Which statement is true about the following vector field? O Vectors all point toward the origin O…

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Q: Identify the theorem: If C is the boundary curve of a surface S in 3-dimensional space, then the…

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Q: Given the national income model Y = E; E=C+I where C= 280 +0.6Y, Io = 80: (a) Write down the value…

A: We need to find equilibrium point.

Q: Evaluate the integral f [[ - Y sin(x²)dxdy.

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Q: Let the vector v have an initial point at (−1, 1) and a terminal point at (5, –5). Plot he vector v…

A: We have to find the component, magnitude and direction of given vector.

Q: In 23 In y SS 10 Evaluate the integral The value is. (Type an exact answer.) ₂x+y dx dy.

A: The given integral,     ∫0ln 23∫0ln yex+ydx dy

Q: A gas station stores its gasoline in a tank under the ground. The tank is a cylinder lying…

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

Q: Evaluate the following integrals: 1. f(cos x + csc² x)dx 2. f(tan x + sec² x) dx 3. (1+sec² x) dx…

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Q: 2. Find the limit and confirm your answer using the sandwich theorem 1 - cos x lim 818 1. 2. 3. 4.…

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Q: (a) Assume that f(x) is a function defined by f(x) = x²-3x+1 2x - 1 for 2 ≤ x ≤ 3. Prove that f(x)…

A: Given.

Q: Question 13 Which of the following satisfies the differential equation d² y dx² A. y = e³r B.y=e-3x…

A: Explanation of the answer is as follows

Q: Let D be the region enclosed by y = eª, y = e¯ª, x = 0 and x = 2. The volume of the solid formed by…

A:

Q: Find the area bounded by the curve y = 4+2x+z² and x-axis from z=-3 to z = -1. Area of the region -

A: y = 4 +2x + x2 A =∫-3-1f(x)dx A = ∫-3-1 4 +2x + x2dx A = [4x +x2 +x3/3]-3-1 A = (-4 +1 -1/3) - (-12…

Q: Find the average value of: f(x) = 9 sin x + 8 cos a on the interval [0, 8π/6] Average value=

A: The average value of fx=9sinx+8cosx on the interval 0,8π6

Q: Δ Ο Ο

A: Given; M=5 units , T=4 units

Q: x-y (x,y) →(0.0) x + y 2.) Prove that lim does not exist.

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Q: 15. Si dt 1³ + 1² - 2t

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Q: Find the divergence of the following vector field: 0 O 2z O O F = (y, -x + z², 3x)

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Q: Find the particular solution of the following differential equations with the given condition. 3) dy…

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Q: Evaluate the integral below by interpreting it in terms of areas in the figure. The areas of the…

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Q: c) A loan of $A is made on 20 April 2015 at a simple interest rate of 6% per annum. The accumulated…

A: Please refer to the image below

Q: π I Find the volume of the region bounded above by the surface z = 7 sin x cos y and below by the…

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Q: A(4) = A'(4) -

A: Integration gives area below curve area above x axis is positive area below x axis is negative A(4)…

Q: J; x² x² - 1 4 dx

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Q: 1000 1+9e-t The number of minnows in a back yard pond is modelled by the equation P(t) = Where is…

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Q: Find an antiderivative F(x) of the function f(x) = 4x² - 6x +5 such that F(1) = 14. F(x)= (Hint:…

A: Solution is given below:

Q: B. For the figure shown below, find the sum of the areas of all the semicircles. 47

A: I am attaching image so that you understand each and every step. Answer is 227π512 square unit