Show that, if f and g are Reimann integrable on [a, b] then f - g is Reimann integrable on [a, b], and S (f-g)(x)dx = S f(x)dx - S g(x)dx. a

Q: Activity IV. Determine the truth value of each item. A. If X and Y are true statements and A and B…

A: Since you have posted a multiple  question according to guildlines I will solve first   question…

Q: 88+88

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Q: Use integral test to determine converges or diverges.

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Q: In Exercises 1 and 2, differential equations and their associated slope fields are given. For each…

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Q: 7. Evaluate the following integrals using the multipi -3 xy dx dy (1i) ye* dx dy (i) y e* dx dy

A: To evaluate the given double integrals.

Q: Four holes are drilled in the circular plate in the figure below. The centres of the holes are 5 in.…

A: Here the given image is                                                          Given that the…

Q: A. Evaluate the following integrals: S tan'x dx 3 1. 4 2. csc* xdx 3. |tan 3x sec 3xdx 4. ſcot'x…

A: "Since you have posted a question with multisubparts, we will solve the first three subparts for…

Q: llustration 25.2: Minimize U = 2x, + 4x, Subject to 4x, + 2x, > 12 3x, + 5x, > 15 5x, + 4x, > 20 *,…

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Q: d Jcose d cose 'cos(r sin 0)]= [e* Telcom sin(tsin 0)]. (i) Show that t. %3D dt

A: (b) (i) show that t·ddtet cosθ cost sinθ=ddθet cosθ sint sinθ consider left hand side  t·ddtet cosθ…

Q: Example 3: Graph f(x) = \x| , and determine the domain and range of s. Solution: S(x) -3 -2 -1 3

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: Given uo, u1, U2, U3, U4 and ug and assuming the fifth order differences to be constant, prove that…

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Q: Given the equations 10x1 + 2x2-X3 = 27 -3x1 - 5x2 + 2x3 = -61.5 X1 + x2 + 6x3 = -21.5 %3D a) Solve…

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Q: The total number of positive integer solution to the equation (x + y + z)(a + b + c + d) = 15 is

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Q: An exercise machine with an original price of $820 is on sale at 11% off. a. What is the discount…

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Q: (b) The curvature k of a curve C at a given point is a measure of how quickly the curve changes…

A: (b) curvature of the a curve is defined as  κ=x'ty''t-y'tx''tx't2+y't232 use parametric equation of…

Q: Find the solution. dy 2y + - :=x?y?sinx dx

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Q: Find the distance between the centres of the holes in the metal plate shown in the diagram below.…

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Q: Find regular singular points of the defferential equation. d²y dy 2x? +(x² - 4) y = 0 +3x dx? dx

A: Given differential equation is 2x2d2ydx2 + 3xdydx + (x2-4)y = 0

Q: Let X ~ Uniform(a, b). Find Expected value EX.

A: Given X~Uniform(a, b)

Q: The following table  shows certain values of xx and f(x)f(x) of a particular function. Use it to…

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Q: Let 1 2 A =| 1 1 2 4 How many solutions does Ax = 0 have? O a. 1 O b. 0 Oc. 3 O d. Infinitely many O…

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Q: Use Laplace Transform technique to solve the initial value problem y' + 2y = 26 sin 3t , if y(0) = 3

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Q: 3. For the following predator-prey system, identify which dependent variable, r or y, is the prey…

A: Given: dxdt=αx-αx2N-βxydydt=γy+δxy To identify which dependent variable is the prey population and…

Q: Show that Q[x]/⟨x 2 − 2⟩ ≅ Q[x]/⟨x 2 + 4x + 2⟩.

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Q: The critical point of the function f(x) = x³ – 5x² + 2x – 17 is %3D - o (용, 1) ㅇ (름, 1) o (음,-1) (금,…

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Q: QUESTION 4 Suppose you are using a triple integral in spherical coordinates to find the volume of…

A: Here we find the range of spherical coordinates.

Q: a.) How far is the man from the information center? b.) What is the equation to represent the…

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Q: Use the Cayley-Hamilton theorem to find constants a, b 5 (-2 and c such that A4= aA² + bA + cl if A…

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Q: Let x be a continuous random variable with PDF 3 x > 1 x4 fx (x) otherwise Find the mean and…

A: Given PDF is fX(x) = 3x4,x ≥ 10,otherwise

Q: Example 1.2 (e) Determine if the following series is convergent or divergent. In n b) d) E S (n+1)…

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Q: 2. Find the eigenvalues and eigenvectors for the following matrices 4 3 a. A = 5 6 1 2 -1 b. А — 0 2…

A: We have to find the eigen value and eigen vector.

Q: 4. Let f(x) = { x/² sin ; (x+ 0) 0; (x = 0) i Calculate f'(0) using the definition. Hint see…

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Q: You are given a technology matrix A and an external demand vector D. Find the corresponding…

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Q: Find the series solution of y"+ (1+x2)y=0 using the power series method.

A: Consider y=∑n=0∞anxn be the solution. Differentiate the expression of y to obtain the expressions of…

Q: Consider the following IVP: y" -3y' -10y = 1, y(0) = -1, y'(0) = 2 Find the general solution. 13 21…

A: Given differential equation is y'' - 3y' - 10y = 1 Here auxiliary equation is D2 - 3D - 10 = 0 D = 3…

Q: 6. 2. 3.

A: Follow the steps below.

Q: Ryan usually bikes at an average rate of 12 miles per hour (mph). How long does it take him to bike…

A: Since you have asked a question with multiple sub parts we will solve the first three subparts for…

Q: Which of the following surfaces cannot be described by setting a spherical variable equal to a…

A: Given,ρ=k , ϕ= k , θ=k To check which one of the given surfaces cannot be described in the above…

Q: y (x + 2y + 2) dx + (2xy + 5) dy = 0

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Q: Given the following: g(x) = 2 + x - x², [a,b] = [0,3], p = 1 a. Verify that the two conditions of…

A: Intermediate value theorem

Q: The Shatzkins are adding a sunroom to their house. They want the sunroom to have area 14.00 m². One…

A: (a) Formula used: Area of a rectangle of length l and breadth b is A=lb. Perimeter of a rectangle…

Q: Find exactly T(t) and N(t) for x = e'cost, y = e'sint, z = e' for t = 0. [Choose the correct…

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Q: Among all the numbers between 20000 and 70000, including the numbers 20000 and 70000, how many each…

A: The total number of numbers between 20,000 and 70,000 is 70,000−20,000+1=50,001. First calculate the…

Q: Consider the matrices 1 0 0 0 0 1 1 1 A 2 0 0 1 0 0 B = 0 0 1 1 1 0 0 0 1 18 5 1 -7 8 C = 0 0 1 0 0…

A: We know, a matrix is in reduced row echelon form(rref) if, 1)In each row first non zero term should…

Q: why ピs{oッ| is Cupve?

A: Solution

Q: Approximate the area under the curve y = x² from z = 1 to z = 3 using a Right Endpoint approximation…

A: Given the curve y =x2 from x = 1 to x = 3  We have to approximate the area under the given curve by…

Q: (; 3s + 8 s2 + 2s +5

A: Some of the properties of inverse Laplace  L-1ss2+a2=cosatL-1as2+a2=sinatL-1F(s-a)=eatL-1F(s)

Q: 3 Show that the series E: is convergent and find its sum. (n+3)(n+4) n-1

A: Simplify the general term of the given series.…

Q: 6. Consider the horizonal strip 2 = {z+ iy : -1 < y < 1}. There exists a holomorphic function f on…

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Q: 2. Use the MVT to show • Prove that the derivative of f(x) = k, on [a, b], where k is constant, is…

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