if 900 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box

Q: Let C be the boundary of the portion of the plane x+y+z=2 that lies in the first octant, oriented…

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Q: 1. Let S be the triangular region in R3³ with vertices at (2,0,0), (0,6,0), and (0,0,3) with upward…

A: we know that triangular  region is part of plane since all the vertices  ( 2, 0,0)  , ( 0, 6, 0)…

Q: 4 Find the arc length of the curve the interval 2≤+ ≤ 5 3 given parametrically by x= 3 + ² y = + ²,²…

A: To find out the arc length of the curve.

Q: Let S = {-2, -1, 0, 1, 1, √2, 2, 4}. Determine which elements of S satisfy the inequality. (Enter…

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Q: Find the directional derivative of w=2x²yz in the direction of v=3i-4j at the point (-1, 1.13)

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Q: Test for convergence or divergence: e me emrin n=1

A: Find the limit as n tends to infinity

Q: Consider the function f(x) = 10√x + 4 on the interval [1, 8]. Find the average or mean slope of the…

A: Given the function is fx = 10x+4 on the interval 1, 8.

Q: Use linear approximation, i.e. the tangent line, to approximate √49.4 as follows: Let f(x)=√x. Find…

A: For function, f  the linear approximation at a is given by L(x)=f(a)+f'(a)(x-a)   ...............(1)…

Q: Determine whether the work done along the path C is positive, negative. or zero. zero Ⓒ positive O…

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Q: Find parametric equations for the line. (Use the parameter t.) the line through the points (14, 3,…

A: Topic- Equation of line through given points

Q: A fence 6 feet tall runs parallel to a tall building at a distance of 2 ft from the building as…

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Q: dr 3 - 4r - r2

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Q: sinx cosx 4 + sin4 x dx

A: The given integral is sinx cosx/(4+sin4x).

Q: 2 Consider the function f(x) = 5x + 4z-¹ For this function there are four important intervals: (-∞o,…

A: Please see the below picture for detailed solution.

Q: Example 1 Find dy/dx, if sin (²+3x+¹) b. y = cos²(2x-1)

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Q: Find the derivative. [미 In dx x +3 x-3

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Q: -2 1. Ella thinks that if a function is positive over an interval, then its derivative is also…

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Q: You deposited $50 into a bank that offers 2.5% interest for 30 years. A: What is simple interest…

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Q: Find the solution of the given differential equation. dx 1 y²-6y+13 dy = 0 Express your answer…

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Q: If R = {(x, y) : 0 ≤ x ≤ 1,0 ≤ y ≤ 1}, then find (²+1) +2 0 1 arctan O 2√2 3 0 √2 3 O √2 3 (√³/₂2)…

A: Please see the below picture for detailed solution.

Q: Find lim a. lim x→0* c. lim x²- - 5x + 6 2 3 x - 3x x -5x+6 b. lim x+3+ x³-3x² 2 x -5x+6 x³ - 3x² X…

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Q: Find r'(t). NOTE: Enter your answer in terms of i, j, and k. r'(t) r(t) = (tan−¹(5t))i+t cos(t)j —…

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Q: Use linear approximation to estimate the amount of paint in cubic centimeters needed to apply a coat…

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Q: For the function f(x) = 3x² −x³ – 4 where −3 ≤ x ≤ 3, complete the following. 1. Find f' and f". 2.…

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Q: [ (x − 7) sin(x) dx

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Q: What is the horizontal distance from point E to the Vertical Axis? feet

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Q: lim-(In(5n³-n+1)-in(7n³n+1)) 3 3

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Q: incorrect

A: To find dy and to evaluate when x=-5 and dx=0.4 for the function y=2x4-45x+1.

Q: Find the G.S. about xo = 0 for the following DE's (x²+4)y" + 2xy' - 12y = 0 1.

A: Please see the below pictures for detailed solution.

Q: 2. Evaluate the following limits. DON'T USE L'HOSPITAL'S RULE IN LIMITS! (a) ( lim√2-2-1 =? (b) lim…

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Q: Admission to a baseball game is $3.00 for general admission and $6.50 for reserved seats. The…

A: This question can be solved using the concept of system of linear equations.

Q: 1. A private telephone company serving a small community makes a profit of *12.00 per subscriber, if…

A: “Since you have asked multiple questions, we will solve the first question for you. If youwant any…

Q: Evaluate r2 ff dyda.

A: Given itegration ∫-12∫x2-2x   dy dx

Q: Solve the following initial value problems: A. y(0) = -3: y= B. y(0) - 6: y= dy dt 2t

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Q: Example 1 Find dy/dx, if a. y=sin(x² + 3x + 1) b. y = cos² (2x-1)

A: I have stated the used formulas in the solution

Q: jw F(W). jwF(W) = jw F(W) = - A -[2-acos (WT)] Tjw -2A (1 - cas (NT)) трия -2A (asin" (WI)) TJw (( a…

A: To find how we reach at the final step.

Q: a. b. n=1 8 n någn-1 (-5)n 1 nVn? +1

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Q: sinx cosx 4 + sin¹ x X dx

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Q: ex + ex 11. y=e-ex

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Q: da Find at z = 4 if y = 4z² - 1 and dt da dt 11 > Next Question dy dt = -5. 11

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Q: 8] n=1 1 n√n +1

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Q: Find the average value of the function over the given interval. F(x) = = 2₁ [4, 6]

A: We have to find the average value

Q: Find the Taylor series for f(x) centered at the given value of a. [Assume that f has a power series…

A: We will find the required.

Q: 50. y = 1/√; y(iv)

A: We can find the 4th derivative as below

Q: (b) Determine whether the series Σ n=1 5n cos(3n) 2en converges or diverges.

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Q: 11 Let f(x) = 7x-6 +2 Find the open intervals on which f is concave up (down). Then determine the…

A: Solved below.

Q: An object is moving on a horizontal line such that its acceleration at anytime t is given by…

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Q: Find the particular solution of the differential equation that satisfies the initial equation= f(x)…

A: We have differential equation f"(x) = 7/x2  and initial conditions f'(1)=3 and f(1)=4

Q: Evaluate 4 R³ TR³ O TR³ O TR² 2π 0 R p² sin odpdøde.

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Q: Express the following endpoint sum in sigma notation but do not evaluate them L10 for f(x)=square…

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