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Q: 3. Find the volume of the solid generated when the region enclosed by y = √2x+8, y = x, x = 0 is…

A: To find the volume of solid generated when the region enclosed by y=2x+8, y=x, x=0 is revolved about…

Q: 2- Let f: [-2,2] → R be defined on [0.2] by f(x)= {2 prove that f is Riemann integral. X≤0 x < 0

A: Given : f : [-2, 2] →ℝ defined as   f(x) = 3x≤02x&gt;0. To prove : f is Riemann integrable.

Q: One of the following is a general solution of the homogeneous differential equation y" - y' - 2y = 0…

A: To find the given solution :-

Q: Q3. Find the cross product of the vectors and .

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Q: 2: A necessary condition for a function to be unimodal on the interval [a, b] is that strictly…

A: Statement: A necessary condition for a function to be a unimodal on the interval [a,b] is that…

Q: 6. Check the convergence of the following series: 8 n (a) (1+-!-)" 2

A: As per the company guidelines we are allow to solve one question at a time so i am solving first one…

Q: Find the Maclaurin series for f(x) = ex+x² using the familiar series. Then use the results to…

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Q: i. f(x) = 8e* - x7. ii. f(x) = e cos 3x.

A: These are the questions from the application of derivative.

Q: H.w1: evaluate fe* siny dx dy i) using the trapizodial rule in both direction, Ax= Ay = 0.1 ii)…

A: please comment if you need any clarification. If you find my answer useful please put thumbs up.…

Q: 8: [1 The matrix A = 4 L3 O True O False -2 31 1 -1 - 2 is a positive definite matrix. 21

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Q: If u and v are the two solutions of d'y dy dx² + P + Qy = 0 dx uv₂u₂v + P (uv₁u₁v) = 0 (uv₁ - u₁v) =…

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Q: Question 2. Let E be the solid region inside the surface x² + y² + z² = 25 and above the surface z =…

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Q: Investor Dan has $119,000 to invest in bonds. Bond A yields an average of 9.4% and the bond B yields…

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Q: A tank initially holds 80 gal of a brine solution containing 1/8 lb of salt per gallon. At t=0,…

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Q: 8: What are the values of k E R for which the function f(X) = -2kx² + x₁x² + 4x will have a strict…

A: Let us solve the calculus problem in the next steps.

Q: 7. Let x₁ = a > 0 and Xn+1 = x + 1/x,, for n E N. Determine whether (x,) converges or diverges.

A: Q7 asked and answered.

Q: y = ae²x y = ae + be + bela -12 on to the nonhomogeneous equation y" - y' - 2y = -6e y = 12e² y =…

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Q: Find the greatest common divisor of the polynomials. f(x)= x³-11x²+24x+30 & g(x) = x² - 12x +35.

A: We have to find greatest common divisor of Given polynomial function.

Q: 1 ++²)

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Q: Q4. Find dz/dt where z = 2xy - x² y² and x = 2t, y = t²

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Q: 2. The diagram below was created using equilateral triangles congruent to ABSR. If OS=a and OT=b),…

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Q: companies that sell identical products. Compan or Php 27. Meanwhile, Company 2 can sell the e…

A: Game Theory is the study of decision making strategies of two individuals or agents where their…

Q: 1. Find the numerical Integration of cos(x) + sin(x) where n = 4 using trapezoidal rule.

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Q: Given the following matrices. Solve for the following: 15 25 58 81 2 14 A= 10 11 5 B = 42 3 -1 -6 42…

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Q: (c) Calculate dx √x(x+1)

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Q: 5 the following Tuation Sutisfied Cauchy - Rieman. equation 4 W = Z Z" سر

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Q: 1. A system is composed of a rod and a disk, as shown at t = 0 below: 6 -6 4 6 -2 -4 -6 The axes…

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Q: a Show how Pip can complete the circuit by adding less than 120 cm of track. b Show how Pip can…

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

Q: 1. Let X be a topological space and be an equivalence relation on the elements of X. Define : XX/~…

A: Given: πx=x To find: Solution

Q: Let f(x) = (x + 1)² - 1, x 2-1. Then the set {x:f(x) = f(x)} is

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Q: y = -x^2 + 4x, y = x^2 - 6x + 5, x=0, x= 1 O 2.012 sq. units O 2.022 sq. units O 2.032 sq. units…

A: We have to find the area of the bounded region.

Q: Solve using Power Series Centred Around Zero. (X²− 1) X² y“ - (x²+ 1) y` + (x² + ₁) Y = O

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Q: The graph of the function f(x)=cotxf(x)=cotx is given above for the interval x∈[0,2π]x∈[0,2π] ONLY.…

A: One sided limit of a real valued function comes when the independent variable moves towards the…

Q: Let f : [0, 1] → [0, 1] be continuous. Show that there exists an element x = [0, 1] such that f(x) =…

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Q: 1 (i) Show that 2x-1 is a factor of 2x³-5x2 + 10x -4.

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Q: Compute the derivative: a. r(t) = b. r(t) = sint cos ti - t4 In t²j

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Q: 7. By separating a) b) the variables convert the PDE into a system of ODES Sem азт а т + д?хду дхду…

A: The given problem is to convert the given partial differential equations into the system of ODEs by…

Q: 4. Classify the type of the equation as elliptic, parabolic or hyperbolic. Uxx xuy+xu 0 =

A: The given problem is to classify the given partial differential equation as elliptic, parabolic or…

Q: Find the exact values of the remaining trigonometric functions of satisfying the given conditions.…

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Q: Classify the series as absolutely convergent, conditionally convergent, or divergent. (-1)+¹k! (2k -…

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Q: Use the Laplace transform to solve the initial value problem where y'' - 3y' + 2y = f(t), y(0) = 0,…

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Q: Direction Fields Plotting Direction fields can be done using the function quiver: quiver Quiver…

A: We will use matlab code given in the question

Q: The intensity of light I (measured in luxes (lx)) at depth y (in m) below the surface of a lake can…

A: You post more than three subparts questions, as per our guideline we can solve only first three…

Q: Let 21 = 8(cos(190°) + i sin (190°)) and Z2 = 17(cos(14°) + i sin(14°)). Compute each of the…

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Q: Draw a left endpoint rectangle approximation of the area with n = 8. How do Ax and the change? O O…

A: The given function is fx=-x2+6x-7 To find:the area by mid point rule.

Q: The table below reports the quantities and prices for a fruit basket consumed by RMIT students for…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: Consider the function Ha(x) defined on [0, π] as Ha(x) = a 0 and as t → 0.

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Q: Q3. Find the polynomial f (x) by using Lagrange's formula and hence find f(3) for X: 0 1 5 2 2 3 12…

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Q: 6: [1 The rank of the matrix A = 4 15 True O False 2 2 5 7 31 6 is equal to 3. 9

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Q: 12. Solve the following system of equations using either the substitution method or the graphing…

A: Introduction: The equations belonging to a system of linear equations represent a line in Euclidean…