give the formal proof of validity

Q: Find the upper Riemann sum U(f.P) and the lower Riemann sum L. P) for each of the following…

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Q: FINITION MATCHING - Match the definition (A, B, C...) in the right column with the correct term the…

A: Solution

Q: Use Green's Theorem to evaluate the line integral along the given positively oriented curve 5y³ dx -…

A: We know that , Green's theorem ,  Consider C be a positively oriented  , simple , closed , piecewise…

Q: III. Consider the parabola C: z-4 = -(x - 2)² on the xz-plane. 1. Find the center-radius form of the…

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Q: 5- Find the Maclaurin series generated by the following function: f(x) = sinh(x)

A: Sol

Q: in fuzzy graph What is the fuzzy trees ? And give an examples

A: We have to define fuzzy tree with example.

Q: F(s) = = S (s+1)5

A: We find the inverse laplace of  F(s)=s/(s+1)5

Q: Example 3: Find the parametric and symmetric equations of the line passing through the point (-3, 5,…

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Q: Solve the differential equation 3y + 3y (sin-¹x)√1-x² : 1

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Q: Q4- Solve the following differential equation: (1 + x²) dy + -(y- tan ¹(x)) dx = 0

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Q: Q3- Sketch the region of integration and evaluate the integral: In8 Iny ex+y dxdy

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Q: 2. The Dual model a. Is derived systematically from the Primal model b. provides the decision maker…

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Q: Solve the following differential equation (√y²+1)dx tan-ly + (xlnx)dy = 0

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Q: The value of the following = (2+ sin 2x3) Using the trapezoid integration dx method, knowing that n…

A: Sol

Q: Let S {(a,b): a,be R, a 0}. Show that the relation R defined on S by (a, b) R(c,d) if = ad be is an…

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Q: Find the smallest number of colors that can be used to color the map. So that any to state sharing a…

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Q: 1. Consider a circle of radius 6 with center at the origin. a. Lines with slopes 1 and -1 each…

A: The point symmetric about x-axis of (x,y) is (x,-y) The point symmetric about y-axis of (x,y) is…

Q: 1. Which of the following statements is (are) true? I. If f is a function from [a, b] to R and F is…

A: Please see the attachment

Q: Prove: if a₁, a2, ... an are n ≥ 2 real numbers such that a₁ a2 ... .an=0 then a₁ = 0 for some…

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Q: 2. Using laplace transforms solve for x and y: dx dy + dt dt 2dx dy + + x +y = 3 dt dt subject to…

A: The solution is given as

Q: Consider the force field F = (3x²yz - y + z, x³z - x, x³y + x). (a) Verify that it is a conservative…

A: A vector field will be conservative if its curl is zero . If f is potential function of F then ∫abF…

Q: Determine whether the equation is exact. If it is exact, find the solution. (e*siny + 4y)dx - (4x -…

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Q: Find the first four terms of power series solution of the given differential equation (x² − 1)y" +…

A: Given DE is (x2-1)y"+6xy'+4y=-4 .......(1) We find the first four terms of the power series solution…

Q: 3. Solve, showing details: y₁ = 4y2 + 5et y2 -V1-20e-t yı(0) = 1, y2(0) = 0

A: Sol

Q: Prove that sin²x x cos²x x= csc²x-cot²x 4csc²2x

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Q: Solve for y esec(4y²−6y+14) = 3x + 1

A: If p=sec q, then it can be written that q=2πn+sec-1π and q=2πn-sec-1π, where n∈Z. Using the…

Q: Find the volume of the solid generated by revolving the area bounded by x² - 2kx - 4ky + k² = 0 and…

A: Using cylindrical shell method

Q: A dog house has a shape of a regular heptagon. Calculate the size of each of its exterior angle.

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Q: Let u = (a11, a12, a13), v = = (a21, a22, a23), w = (a31, a32, a33) be three vectors in R³. Explain,…

A: Here we use the orthogonal property.

Q: Find the coordinates of the centroid of the solid generated when the smaller region bounded by x² +…

A: Solution:   Given data, x2+y2-6ax=0x+y=6a we have to find centroid of solid formed by above equation…

Q: Which of the following is the homogeneous differential equation? A. (3x - 5)dx = (4y - 1)dy B. xydx-…

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Q: x sinx find dy for y dx √(x-1) (x²+1) Evaluate f(u² + 2u + 3)² (u + 1)du

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Q: (a) Compute the determinant of the matrix by expanding along the second row (b) Compute a row…

A: We have: A=21-250146251-24215 Part (1) Finding the determinant of the matrix by expanding along the…

Q: Find the volume of the solid generated by revolving the area bounded by x² - 2kx - 4ky + k² = 0 and…

A:

Q: Determine the surface area generated when a portion of the curve in the 1st quadrant of y² = 9(x² -…

A: Please see the attachment

Q: Is the given differential equation =etty separable? If so, how does the equation separate? A. This…

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Q: Find the differential equation whose general equation is y = C₁x + c₂ex. A. (x-1)y" - xy' + y = 0 B.…

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Q: Determine y(t) y" - 13y' + 40y = 0, where y(0) = 0, y'(0) = -2

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Q: A partial differential equation has A. one independent variable B. two or more independent variables…

A: Definition of the  partial differential equation :  A partial differential equation is a…

Q: 3. Which of the following equations is (are) true? 1 I. | 254 = Arctan (5) + x² 25 O I only O II…

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Q: 27. Let f(x)= [x²/3]. Find /(S) if a) S-2, 1, 0, 1, 2, 3). b) S= (0, 1, 2, 3, 4, 5). c) S = (1,5. 7.…

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Q: Let n ∈ Z. Prove that if n is divisible by 3, then n = 6k or n = 6k + 3 for some integer k.

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Q: = A. فأوجد ما يلي: 2 4 0 1 -1 -3 -1 -1 0 2 1 1 1 3 4 ) إذا كانت a) رتبة المصفوفة. b) معكوس المصفوفة.…

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Q: k 3. The intensity of the illumination, I, on an object at distance x from a light source is where k…

A: Apply differential  y=f(x)   ∆y=(dy/dx)∆x

Q: For items 13, 14, and 15, consider the region R bounded by y = Arctan x, r = 1, and the x-axis.…

A: Use the following formulae, to calculate the centroid of the area bounded by the curves x=fy and…

Q: b) Consider the following LP problem. Minimize z = 2x₁ + x₂ Subject to 3x₁ + x₂ ≥ 3 4x₁ + 3x₂ ≥6 x₁…

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Q: The Cartesian coordinates of a point is (4, -4√3). This point in polar coordinates can be…

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Q: 1. If f is an increasing function on (a, b) and P= (ro) is any partition of [a, b], prove that sup…

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Q: Given the activity network below with ini- tial activity A and final activity F, what is the minimum…

A: Given :- Given that the network with initial activity A and final activity F To Find :- To find…

Q: 4 3 3 Let A = -1 1 0 4 4 5 Use determinants to decide whether the matrix is invertible. Enter the…

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