1. "Let fE a[a, b]. For x E (a. b), set F(x)=ff. Prove that F is continuous on [a, b].

Q: 4:15 Homework: 2. Application of Integration Page 1 of 8 Save and complete later Find the…

A: According to Simpson's 1/3 rd rule the integral of a function between the limits a and b is given by…

Q: 5. Let (a) Find the compact SVD of A. +B A

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Q: 4-Let (Z12, +12) be a group and let S={4,6}, find subgroup H generated by S. if exist

A: I have used the definition of subgroup generated by a subset.

Q: 4. Which of the following vertices are adjacent to vertex B? B E F A) AEDC B) AEFC C) AEDFC OD) AEC…

A: Since you have posted a multiple question according to guildlines I will solve first(Q4)   question…

Q: 1. The Maximum point of y= (x²+2x+10) (x-3)

A: We have to find the maximum point of the given rational function. We can find it in two ways, either…

Q: Instructions: Show all your work. Answers with no work will not get any 1. Use induction to prove…

A: The solution of the question is given below.

Q: 1) 0.7 Estimate f(x) dx, 0 from the graph of f. Use the Trapezoid Rule. a) 2 b) 2.25 c) O 22.5 d)…

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Q: (0,4) C R (-2,0) (-1,0) (1,3) (c) Use the WASHER METHOD to set up a (sum of) definite integral(s)…

A: Divides the region into two subregions.

Q: 9) x² + y² + 12x + 22y + 108 = 0 CX+67² + y +117²=49 CX-47² \ Cy-151²=9 CX-107² + (y +1272²=9 CX-5)…

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Q: Find the dimension of the splitting field of each of polynomials x+1 and x² - 2.

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Q: I. EVALUATE THE FOLLOWING LIMITS. SIMPLIFY AND ENCLOSE FINAL RESU 4. Lim (2 4 Arctanx.

A: Solution:-

Q: 1. The Maximum point of y = (x²+2x+10) (x-3)

A: For relative maximum or minimum To maximize or minimize  a function f(x) 1st we need to find its…

Q: 1. Let g: DR be a function on D and (c, ∞o) C D for ome ce R. Then lim g(x) = 1 (1 € R) if and only…

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Q: Suppose that 80 moose were introduced into a wildlife refuge in 2016. By 2020, the population had…

A: Introduction: Exponents are used in the exponential function, as the name implies. However, an…

Q: Is 1/8 - 10 ( 3/4 - 3/8x ) equivalent to -1/8 (59 - 35x )

A: Equivalent expression  To check two expressions are equal means the coefficient of each term is same…

Q: 5. Let R be the relation on the set {1, 2, 3, 4, 5} containing the ordered pairs (1, 1), (1, 2), (1,…

A: Let R be the relation on the set 1 , 2 , 3 , 4 , 5 containing the ordered pairs  1 , 1 , 1 , 2 , 1 ,…

Q: X 1 4 7 9 11 f(x) 12 -23 -15 33 -13

A: Lagrange's interpolation polynomial for n points can be defined as:…

Q: Q.5 Linearize the non-linear system z = x² + 4xy + 6y² in the region defined as 8 ≤ x ≤ 10, 2 ≤ y ≤…

A: Given non linear equation is z = x2 +4xy +6y2 Region :- 8≤x≤10,  2≤y≤4.

Q: d the solution. - 2y'-2y = 0 31 A y = c₁₂e √³1 + B) y = cell-√3)+c_xe (1+/3), -cell-cel+5 Dyce -…

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Q: 1.4. (-) Exhibit a graph G with a vertex v so that x (G-v) < x (G) and x (G-v) < x (G).

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Q: A yacht starts from a harbour and sails for a distance of 11 km in a straight line. The yacht then…

A: Draw and label the diagram depicting this scenario. Use law of cosines to determine the distance.

Q: Let (X, d₁) and (Y, d₁) be metric spaces. Let f: X Y be continuous function, then f-¹(G) is open in…

A: Solution

Q: I. EVALUATE THE FOLLOWING LIMITS. SIMPLIFY AND ENCLOSE FINAL RESULTS. 2. Lim x?cosx sin²¹x 2 x-o

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Q: N 2 (2-1) (2-0.5)

A: The detailed step is given below. We do the partial fraction by first subtracting adding "1" in the…

Q: Show full solution: Find all relative extrema and saddle points of the following function using…

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Q: the set S = [-10, 10] Define the function g on S g(x):= Does g have a maximum and minimum on the set…

A: Taking t =0 ,  g(x) = -x              if x∈[-10 , 0)1-ex                 if x∈[0,10]          g do…

Q: Find of z= In(xy) 8²y

A: For a function of the form: z=f(x, y), the partial derivative with respect to y is calculated by…

Q: Solid S is bounded by the given surfaces. (1) Sketch S and label it with its boundaries. (2) Give…

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Q: [2 1 31 1. If A 4 1 1 3, find A-1 L5 4 21 2. Is the formula valid for matrices? explain why? (A + B)…

A: 1)  We have given that , A = 213413542 We need to find , A-1 . To find the inverse matrix, augment…

Q: A family decide to save some money in an account that pays 9% annual compound interest calculated at…

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Q: Solid S is bounded by the given surfaces. (1) Sketch S and label it with its boundaries. (2) Give…

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Q: Find the moment of inertia: y = x³; x = 1; y = 0 about x = -1.

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Q: 1 Consider the series (-1)-¹ Σ(−1²+ (x+1)* where b is a given non-zero constant. Find the nb2n 1=0…

A: Infinite series: An infinite series is represented by ∑n=0∞ anx-cn, where an is the coefficient of…

Q: The metric subspace ]1,2] of the Euclidean metric space R is a complete metric space. False True

A: Solution

Q: 1 1 b. From (i) prove that, xb + x ² + 1 + x² + x ² + 1 ² + 1 = 1 xa +x+b+1 c. From (ii) given in…

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Q: Find the centroid of the solid bounded by x² = 4y and y = 5x - x² about the x-axis.

A: We will draw the region and rotate it about x-axis to create a solid of revolution . We will need…

Q: B. Determine whether the following definite integrals converge or diverge and evaluate each…

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Q: Suppose the rule ²[ƒ(-2,−1)+4ƒ(−2,0) + ƒ(−2,1)+ ƒ (2,−1)+4ƒ (2,0)+ƒ(2,1)] applied to 12 solve f(x,y)…

A: Given: The rule, 23f-2,-1+4f-2,0+f-2,1+f2,-1+4f2,0+f2,1 is applied to solve ∫-11∫-22fx,ydxdy.   To…

Q: ANSWER 5. For questions no. 4 and 5. Given: Radium decomposed at a rate proportional to the quality…

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Q: Consider the following optimisation problem min f(x, y) = x + y − x2 subject to x + y ≤ 1 x ≥ 0, y ≥…

A: As per the question we are given a optimization problem as : min(x,y) x+y-x2 s.t. x+y≤1 ; x≥0 ; y≥0…

Q: Determine the parametric equations of the curve of of the ellipsoid 4x² + y2 + 4z2 = 4 and the…

A: Solution: Given equation:ellipsoid: 4x2+y2+4z2=4; and half−cone: y2=x2+2z2 To find: parametric…

Q: 1. Evaluate the solution for the following differential equation y" - 2y + y = 2. Find the general…

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: 22. Find the moment of inertia form the given figure. 3

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Q: 5. Lim xsinx x+0+

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Q: Find the general solution of D.E. below: (x-2y) dx + (2x+y) dy = 0

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Q: II. Solve the following problems. Enclose final answer. 5. Given z arctan = (-), 5 Find az/ay

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Q: II. Solve the following problems. Enclose final answer. 4 4. Given z = Find az/ax x+y "

A: Solution:-

Q: Let p». Prove that, for every e > 0, a.a.s. the largest component of G(n, p) has size at least…

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Q: Given F(A, B, C, D) = A'B'C'D' + A'B'C'D + A'BCD' + A'BCD, express F(A,B,C,D) and F '(A,B,C,D) in…

A: Solution: Given that F(A, B, C, D) = A'B'C'D' + A'B'C'D + A'BCD' + A'BCD Now, truth table Row no.…

Q: Find the general solution of the D.E. (y^2 - 2xy + 6x) dx = (x^2 - 2xy + 2) dy = 0 Show your…

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