5. Solve the Euler-Lagrange equation for the functional S [*² subject to y(1) = 1/2 and y(2) (y- yy' + x(y')²)dx, = 1.

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Q: 4. For the function f(x, y) defined by f(x, y) In (√ (√17x² + 11y²) find fax, fyy and fry. Does f(x,…

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Q: 6. Use the intermediate value theorem to show that the function has a real zero between the two…

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Q: looc 7. Given sets A, B and C prove or disprove that (AB) U (B-C) = U (B-C) = (A-C)_

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Q: Exercise 1, Let fla, b] → R be a continuous function, with a, b R, a < b. Call ACR the set of…

A: Kindly refer to Step 2 for the solution.

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Q: 5. (a) Briefly explain why each of the series below either converges or diverges. (-1¹-1 1/2 0 n=1 n…

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Q: Quartely payments aw to be made against  47500 loan at 5.95% compounded annually with a six year…

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Q: the approximations In Mn and S, for 12. Then compute the corresponding errors ET EM, and Es. (Round…

A: ∫0211x4dx=11x5502=11×325=70.4

Q: 5. Prove by induction that for every n 2 1 we have 19 - 13 is a multiple of 6.

A: 5.  Prove by induction that for every n≥1 we have 19n-13 is a multiple of 6.

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A: Manufacturing company has plants in the three locations: Indonesia, Mexico and Pakistan. The company…

Q: 1. AD B 2. Av (CD) 3. ~B~E 4. ~B 5. NA Click or tap here to enter text. 6. C & D Click or tap here…

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Q: Suppose A has row echelon form - 8 - 36 - 36 0 0 0 - 0 0 6 8 – 40 0 - 9 5 6 - 12 The following row…

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Q: QUESTION 7 What is a possible set of values of zfor which sin(z) = j? O z = z = 2nn- jln(√√2 + 1), n…

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Q: Q2 (0 points) Find all basic solutions to the following homogeneous system. 2x +3y +5z +2w = 0 3y +z…

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Q: Find the indefinite integral. (Note: Solve by the simplest method-not all require integration by…

A: Answer :- We have to do the substitution as shown in step 2

Q: Q4. For the f(x)=x²-a, if the initial guess Xo = 2, and the first iteration X₁ =1.875. Find the…

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Q: Find the solution to the differential equations sec³ xdy = csc² y dx y (n) = 514 TT

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Q: 4. For the following two functions f and g, determine go f and fog. f: R → R X → sin(3x) g: R → R &…

A: 4.  Given,          f:ℝ→ℝ,    x↦sin(3x),g:ℝ→ℝ,    x↦,e1x+2if x≠-2πif x=-2. To find gof fog.

Q: Suppose ₁ and ₂ are true mean stopping distances at 50 mph for cars of a certain type equipped with…

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Q: 25) n S sin (+) n s

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Q: Let n=2 and z=-1+i Calculate In (z") Calculate n-In (z)

A: Let, n=2 and z=-1+i, then we have to evaluate:                          lnzn and nlnz

Q: 18. Prove that b b ²1. I 2 a 2 F(x) f(y) dy dx = ( [° F(x) dx) ². [HINT: Notice that 2 b (11(x) dx)²…

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Q: r, s, and t are three consecutive odd integers such that r<s<r. Quantity A r+s+1 Quantity B s+t-1 A…

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Q: Apply the Midpoint and Trapezoid Rules to the following integral. Make a table showing the…

A: Let n be the number of sub interval  then for the integration ∫abfxdx is…

Q: Part 1 Part 2 Evaluate the integral Fdr where F = (ey - sin(x)) and C is the triangle with vertices…

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Q: 3. Let f: R² R2 where f(x, y) = (y³, x + y) and c = →>> = (0, 1).

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Q: (b) Check all of the following that are true for the In(2n)+3n n² series Σ n=1 A. This series…

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Q: If f'(x) = g'(x) on the interval (a, b), then f(x) = g(x) on (a, b). O True O False

A: We find counter example of f(x) such that f'(x)=g'(x) but f(x) ≠g(x) on (a,b).

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Q: Consider the definition of the limit of a sequence in calculus. We can say that the limit of a…

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Q: Evaluate a) 18 b) O 11.2 20 10 3 10 10 3 d) O-18 2y do over the surface S: z = 20 10 3 2/3 1 3 2/3…

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Q: Find a basis for the space of polynomials p( x) of degree :S: 3. Find a basis for the subspace with…

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Q: Find the indefinite integral. (Use C for the constant of integration.) J Ï₁₂-² 11 (z - 12) 11 dz

A: Given integral is ∫11z-1211dz

Q: 1. Find these terms of the sequence (a), where a = 2-(-3)" +5". a) do d) as b) a₁ c) a₂

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Q: Find (a) (fog)(x) and (b) (gof)(x). f(x)=√x-8; g(x)=5x-6 (a) (fog)(x)= (b) (gof)(x) = (Simplify your…

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Q: Can you do this in excel? Please send me to step by step solution. Thanks. This is HISTOGRAM

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Q: 12. Draw a frequency curve for the following data. Monthly Wages (in Rs.) 0-1000 1000-2000 2000-3000…

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Q: 4 Optimization using the gradient What is the largest rectangular prism (in terms of its volume)…

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Q: Find the minimum value of f(x,y)=56x2+21y2 subject to the constraint x²+y²=16

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Q: Which of the following is the area of the region bounded by the graph of the polar equation = 4 + 4…

A: Given the polar equation                        r=4+4cosθ.