7. Determine the dimensions of a rectangular box, open at the top, having a volume of 32 ft³, and requiring the least amount of material for its construction.

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Q: b. S sin (3x) cos¹ (3x) dx

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Q: Given: f(x, y) = ln[1 + x siny] Find: 8² f(x,y) 8x² 2 sin y (1+xsin y)² ○ _ __ sin² y (1+zsin y)²…

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A: We need to consider a section and then integrate accordingly.

Q: Question 2 Evaluate: Express your answer in three decimal places. limx→8 e-2 a-8

A: The objective is to evaluate the limit.

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A: Concept: The formula for the divergence theorem: ∫∫SF→n^ds…

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A: gx=x2+5if x&lt;-23-3xif x≥-2

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Q: 2π -5.² b- - 1 do (1 + tan²0)³ 0

A: See this solution in below

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A: In this question, we need to find the second partial derivative of the given function.

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Q: Calculate the differential equation dy dt and (i) Show and 3 y (π) 2 general solution + 3t² y = cost…

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Q: d- d³y dx3 d²y +69² y dx² - dy 15- dx 100y = 0 equation

A: Topic = Differential equation

Q: 8 What is the lim+2+ (2²4-²2)?

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A: Given :   Continous and differentiable functions

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Q: x²-3 (x-1)² Analyze and sketch the curve given by f(x)=- 2(x-3) (x-1)³ · if y'=—- and y"= 4(x-4)…

A: Given

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Q: Given: f(x, y, z) = e¯ª sin(yz) Find: ² f(x, y, z) əyəx O z cos(yz) et O cos(yz) e O-ze-* cos(yz) O…

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Q: 10 Let u= (1, 2, -1) and v= (3,-1,2) be two vectors in Rª. Which of the following is a normal vector…

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Q: Use the Trapezoidal Rule, the Midpoint Rule, and Simpson's Rule to approximate the given integral…

A: Solve the following

Q: olve the differential equation y"+4y=sec(2t).

A: To solve the following differential equation  y''+4y=sec(2t).

Q: Evaluate: lim-0 (cos 2x) 2²

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Q: 3. 21 ) f(x) = 3x + 1 [1,3] n=3 a=1 right left & middle hand rule b=3

A: To find out the left, right and midpoint riemann sum.

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Q: (a) [In(4) - 2e¹³] dx d b) dx d (c) [2²² - 1 (2²)] = 4e³x In(x [sec (12r) + tan-¹(2x)]

A: NOTE: Refresh your page if you can't see any equations. .

Q: Solve the given differential equation by finding, as in Example 4 from Section 2.4, an appropriate…

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Q: using determination of integrating factors y (y^3-x) dx + x(y^3+x) dy=0 Attpemt only you can solve…

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Q: X-2 lim = 2 a. By L'Hopital's Rule, x→² X²-1 1 1 lim = x→2 2x 4

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Q: 7. Find the volume of the solid generated by revolving about the x-axis the region in the first…

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Q: What is the limo+x².In(x) For answers that are fractions infinity negative infinity write... in…

A: L' Hospital Rule  :   If limx→a f(x)g(x) = 00 and ±∞±∞ form , then               limx→a f(x)g(x) =…

Q: Given w= y² arctan(xyz) + 2x ln(xz). Determine მყ მთ = y + 2y arctan(xyz) + 2x ln(xz) = y[2…

A: We can solve this as follows:

Q: What is f(2022) (cos x), the 2022nd derivative of f(x) = cos x? COS X sin a sina

A: To find 2022nd derivative of f(x) = cos(x).

Q: d. y'"-6y" + 12y' - 8y = 0

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Q: Which one of the following is the gradient of the tangent line at the point (5, 1) on the graph of,…

A: To find the gradient of the tangent line of the point (5,1) on the graph of x+xy+2y2=12 Formulae…

Q: 5. Based on sales data over the past year, the owner of a DVD D(p)-40-2p where D(p) is the number of…

A: answer is in next step.  Since you have posted a question with multiple sub-parts, we will solve…

Q: Considering a continuous function f(x) = 2e³-¹ – 2x, which is true about the relative extrema of f?…

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Q: f(x)= √x-2x √√x X ; f(x)

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Q: e2x (x²-4) Given: y = Determine the following: a. Symmetry b. Intercepts c. Vertical Asymptote/s d.…

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Q: Find all the local maxima, local minima, and saddle points of the function f(x,y) = x² + xy + y² +…

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Q: For the function y = (x - 2) lnx, what are the two x intercepts, and between the two intercepts, is…

A: The given function is y=x-2lnx. For x intercepts we take y=0 and then we solve for x. If y''(x)&gt;0…

Q: What is the derivative of y = 3x6? 2x6 2x5 18x6 18x5

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Q: dx What is , where dy' x³ + y³ = 3xyusing differentiation? implicit dx dy y-x² y² +x dx y-x y²-x dy…

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Q: (y³ - 3x²y + x³ - 4x) dx + (3xy2 - x³ + 8y³ +y + 5) dy = 0 I. f(x, y) = M(x, y) dx + g(y) II. Find…

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Q: 2. Find the volume generated by revolving the area bounded by the parabola y² = 8x and its latus…

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Q: does xy=4 describe y as a function of x?

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Q: What is the lim+∞0x².e-²? For answers write... that are in decimal form and round off fractions to…

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