Using Optimization in Derivatives, solve the following question: An open-top box is to be constructed out of a sheet of carton with a dimension of 2m x 1.5 m. What should be the dimension of the box to maximize its volume?

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Q: The equation of motion of a train is given by dv mk (1-e")-mcv dt m %3D where v is the speed, t is…

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Q: 2.61 Let fn(x) = n 1. Prove: fn 0 uniformly on R.

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Q: The particular solution of the following equation by using the D Operator y" + 2y' + 3y = -2x + 3

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Q: Consider the curve C with parametric equations Sæ(t) = t³ – 3t + 1 ly(t) = t(t + 1) %3D %3D defined…

A: 1. Given that,Curve C is given by the parametric equations,x(t)=t3-3t+1y(t)=t(t+1)The curve is…

Q: solve for the laplace transform of f(t) =D {2,t < 플 {-을, 플 <t<ㅠ 6. -e + He i a. 2s 48 2/4 b.

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Q: y' = e2y

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Q: for the following system of differenti d.x = 2x + 2y + z, dt dy = 6x – y + 3z, dt da

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Q: Suppase thut and such that (x?fH f'x) + 3x F(x) on and It exe If t i frowa Oh frow a

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Q: Determine the 1st and 2nd degree Taylor polynomials L(x, y) and Q(x, y) for f (x, y) = x e-a-y"…

A: Consider the given function fx,y=e−x2−y2cosxy. We have to determine the first and second degree…

Q: 2. Sole Laplace's equation for a rectangular region (0<x<1, and 0<y<1) subject to the given boundary…

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Q: 2.50 Prove: A function f is bounded if and only if || f |lsup < o. (Hint: See Definition 2.4.1.) 2.4…

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Q: in fuzzy graph theory What is the compliment And give examples

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Q: 2л — Зу — 7 1. The linear system has –4.x + 6y = –15 (a) no solution. (b) a unique solution. (c)…

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

Q: (1) (a) Use a double integral to find the volume of the solid that is bounded above by the plane z =…

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Q: Q1) solve ÿ – xỷ = (2 – x²)e* y(0)=0, y(1)= e' , h=0.25

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Q: Use a trigonometric solution to find the magnitude of the resultant of the following coplanar…

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Q: Solve the linear differential equation dy 2y x2 %3D - dx 1+x2

A: Given differential equation is dydx - 2yx = x21+x2

Q: ) y"+4xy'+C4x²+ 2) y = 8ë + Ax^424

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Q: 2. Write the Kolmogorov backward equations for a birth-and-death process with birth rates d = 3(i +…

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Q: IF m*n DENOTES 2m – n², FIND THE VALUE OF: ii. -3 * V 5

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Q: 5. Use a trigonometric solution to find the magnitude of the resultant of the following coplanar…

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Q: Question 4 Please simplify this fraction to its lowest terms 290/580

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Q: Example 2: A food product is made from soybean meal (50% protein, 10% moisture) and corn flour (10%…

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Q: х%3D —у? апd x %3D у — 2

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Q: Given A E Mmxn(F). Prove that (LA) = LAt.

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Q: Find the laplace transform of F(t)= 2t^4-3e^2t+10sin3t

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Q: Q4. K=0 K=1] K=2 | K=3 K=4 L=00 L=10 L=2 | 0 L=30 L=4 0 2 24 2 6 28 8 16 24 332 18 36 54 72 32 64 96…

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Q: 5. The elementary row operation E52(-3) was applied to a matrix A obtaining a matrix B. Which…

A: 5. The given elementary row operation is E52-3. To find: the row operation to get A back from B.

Q: 3:.A card is drawn from a well shuffled pack of 52 cards. Find the probability ol: (iv) a card of…

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Q: Laplace transform of (e-t sin? t) 1 2 (s + 1)(s² + 2s- 4) (s + 1)(s² + 2s + 5) O Option 1 O Option 2…

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Q: Question 5. Consider n f (x) = exp (A;t;) i=1 where the A; are real numbers that are either positive…

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Q: k+ 2W+メ+4+2 =5 サ W+ 2x + =

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Q: | (ах с) (2а+b—4c)| (αx b) . c If a = 2i + 3j – 5k,b = 3i + 7j - k and c = 5j – k. Calculate %D

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Q: Prove that if a and b are both positive, and a2 < b2 then a < b          (Use Indirect Proof)

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