An open box is made from a square sheet of cardboard, with sides 3 meter long. Squares are cut from each  corner. The sides are then folded to make a box. Find the maximum volume of the box.

Q: 1. Given the region bounded by the following functions as well as the x-axis: y= 2²/1₂ ² x= x = 4…

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Q: Find the k-component of (curl F) for the following vector field on the plane. F = (Xex)i + (8y ex)j…

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Q: Integral Evaluate the √x (x-²) ³ dx

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Q: hich among the sets is open? (,1) 1/n.....1/3,1/2,1}

A: Open sets are those sets which does not include the indicated values.

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Q: Kindly answer the question and provide a clear and correct solution. If I still get wrong…

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Q: 5. Let D be the region bounded by the lines y = x, x = 3 and the curve y = 1 (a) Sketch the region…

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Q: y = 4x² from x = -3 to x = 3.

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Q: Consider the function f(x) = 3 - 3x², 3 - 3x², 4 ≤ x ≤ 1. The absolute maximum value is and this…

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Q: s projected that x years from now the population of a certain city will be changing at the rate of…

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Q: 2. Evaluate da da d. Java [. 2 / + 3 + a r/Mr | 1 | dr ar/rº +1

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Q: ¹In(1 + x) -dx X

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Q: Are Lebesgue integrals always finite?

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Q: 2 . show that V(x,y) = x 'f (2x+y) is the general Solution of: av X du 2X 1 = V ду dx

A: To show that, vx, y=x f2x+y is the general solution of: x∂v∂x-2x∂v∂y=v

Q: calculate the area of that part of the surface z = 2xy which is bounded by the planes   x+y=1, x=0,…

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Q: A certain drug is being administered intravenously to a hospital patient. of the drug enters the…

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Q: ¹In(1+x) -dx X

A: According to guidelines we must answer only one of the multiple questions given. So, I answer only…

Q: Determine the x-coordinate of the local maximum of the curve y = (2x - 1)2 (3x+4) in the interval…

A: Given: y=2x-123x+4

Q: f(x) = 4√x + 2x1/2 – 8x-7/8 + x2 1 23 +2

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Q: Use Green's Theorem to find the counterclockwise circulation and outward flux for the field F =…

A: Here, the outward flux is given by: ∫∫DDiv(F) dA…

Q: Evaluate the indefinite integral Sxe-xdx O-X-1 ex O X-1 ex O -x+1 e-x O-x-1 e-x -X =+C + C = + C - +…

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Q: F Find the area of the region bounded by the curve y = x³ and the lines y = -x, y = 1. (Draw the…

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Q: Select the following sets of parametric equations that describe the parabola y = x² x=t, y=t² □ y =…

A: To select the follwing sets of parametric equations that describe the parabola y=x2.1 x=t, y=t22…

Q: dy Write down a differential equation of the form dt all other solutions diverge from y 9 as t →∞. =…

A: The differential equation has a form dydt=ay+b whose all other solutions diverge from y = 9 as t→∞

Q: Problem 4. (. Let C be the curve given by parametric equations x(t) = t², z(t) = lnt, t€ (-∞0, +∞0).…

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Q: Michael was sketching ngl the graph of f(x). He lost part of his notes including the equation of the…

A: Michael was sketching the graph of fx.Partial information is given.Domain of fx: ℝx-intercept are at…

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A: We have to choose the correct option from the given options according to the given information

Q: Set up the integral in terms of h(x) that evaluates the shaded area under the curve and evaluate…

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Q: Which of the following graphs is the correct plot of y = 5+ 5 4 4 -3 3 2 2 -1 + 5 6 2 4 -1 -2 --3-…

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Q: 1 -~-² ( 5 (52² + 4) = = = √( ² ) 6' +4' sin2t.dt

A: As per the instruction, we will be answering the first question. For (1), We need to verify the…

Q: Consider the basis S - (V₁, V₂) for R², where v₁ - (1, 1) and v₂ - (1, 0), and let T:R² R² be the…

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Q: Newton's law of cooling states that the temperature of an object changes at a rate proportional to…

A: We know that, Newton’s law of cooling is given by, dT/dt = k(Tt – Ts) Where, Tt = temperature of…

Q: Given the properties of the natural numbers N and integers N (i) m, n € Z➡➡m+n, m-n, mn € Z (ii) If…

A: We are allow to solve one question at a time. If you need rest of answer then upload separately.…

Q: convert the Following differential equation into a perfect equation and then Find its general…

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Q: By Maclaurin series expansion, show that the sum of the geometric series may be written as a power…

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Q: Include intercepts and restrictions. Show all calculations.

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Q: Determine the constants c and d in the equation of the curve y = ax + b³ + cx+d having a critical…

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Q: Please answer with complete solution. Let A be the curve containing of the line segment from (0, 0)…

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Q: these is closed? OnA_n where A_n=(0,1+1/n) OnB_n where B_n=[0,1+1/n) OUC_n where C_n= [(2n+1)/n, 3]…

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Q: 8) If f(x) = x(x-1)^3 , then which of the following statements is correct? A) f(x) has a point of…

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.) COS(π/X9) dx x10 Need…

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Q: Given a second order differential equation d²x dx 3: + 2x = 2e³t dt² dt dx where t = 0, x = 5 and =…

A: The given differential equation is: d2xdt2-3dxdt+2x=2e3t  where x0=5, dxdtat t=0=7.The above…

Q: s] Set up only an iterated double integral that gives the volume of the solid enclosed above by the…

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Q: Y 3 -3 -2 -1 2 1 -5 1 2 3 4 -1 -2 -3 The function graphed above is: Increasing on the interval(s)…

A: If value of y increases as x increases then function is increasing in that interval. If value of y…

Q: ferential √226

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Q: Use the graph below to fill in each entry of the grid with positive, negative or zero. y = f(x) f''…

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Q: Evaluate the double integral: L y 1/3 27 +1 dx dy.

A: Given: I=∫08∫y132yx7+1dxdy The region bounded by the curves x=y13, x=2, y=0 & y=8 is as shown…

Q: Consider the function ƒ(x) = 2x³ + 9x² − 60x+8, − 5 ≤ x ≤ 3. This function has an absolute minimum…

A: This question is based on application of derivative.

Q: Newton's law of cooling states that the temperature of an object changes at a rate proportional to…

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