Find a number in [0,1] such that the difference of 1/3 the number from its cube is minimized. choices: a. 1 b. 1/6 c. 0 d. 1/3

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A: Given :xe2ydy+x2+1xdx=0

Q: Evaluate the following integrals. (a) (b) Sx√4 x√4 + x² dx

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Q: 1. Determine the value of each of the following limits if they exist. 1²-21-8 +¹ -1 X 3a) lim- b)…

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Q: Calculus I

A: Differentiate and put the respective values.

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A: According to our guidelines we are supposed to answer only the first question if you want any…

Q: 2|6x + 4 ≥ 1 OX- 7/12 O-7/12 - 12/7 choose the right ans оо

A: solution:-26x+4≥16x+4≥12using properties of modulus6x+4≥12  or  -6x+4≥12 6x≥12-4  or  -6x≥12+46x≥-72…

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Q: In (x-2)² In sketching y determine the intersection of the curve and the horizontal asymptote. None…

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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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Q: Q.1- Evaluate the following integrals (answer two only) a- So √x e-√x dx 1

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Q: An ice cube is freezing in such a way that the side length s, in inches, is s(t)=t+6, where tis in…

A: Write down the equation of the volume.

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: af 2 Given f(x, y, z)=x√√x² - yz. Determine дz' af xy Əz 2√x²-yz af s af əz af Əz = = = 2√x²-yz…

A: A detailed solution is given below

Q: 8) y(y³- x) dx + улу x(y² + x) dy = 0

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Q: C. 6x³ +11x² - 4x -3/5 18x² +22x-4dx

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Q: Solve the differential equation. 7. (cosx cosy – cotx) dx – sinx siny dy = 0

A: This is a problem related to differential equation. Based on the general formula and concept we will…

Q: How do you evaluate this integral using trigonometric substitution?

A: Here x2 -a2  type we use trigonometry substitution by x=a sec(θ)

Q: 4) y(2xy +1) dx - xdy = 0

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Q: PROBLEM: The area in the first quadrant bounded by x2-8y, the line x=4 and x-axis is revolved about…

A: Use washer method

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: A large boat is pulled toward a dock by a rope. The rope is attached to the bow of the boat which is…

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Q: Evaluate the line integral y² dx + x²y dy where C' is the rectangle with vertices (0,0), (5,0), (5,…

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Q: 6. Find the volume of the solid generated by revolving about the y-axis the region bounded by the…

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Q: 50 own. Draw the graph of y=g(2x).

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Q: y=? € x ² y² + (y²) ² = 11 - U

A: see below the solution and calculation

Q: Evaluate the surface integral f F.dS where F(x, y, z) = yz i+zxj+xy k and S is the S surface z =…

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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: Q.2-Solve the differential equation (answer three questions only) lo d. y""-6y" +12y' - 8y = 0

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Q: Use first principles definition of the derivative to find f'(x) for the function 3 f(x)= x-2 =

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Q: Find the angle ? between the vectors. (Give your answer correct to 3 decimal places.) u = 7i − 9j +…

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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: d- dx3 ax d² y dx² +6- 15 dy dx Q.2-Solve the differential equation 100y = 0

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Q: find  the area of the  region bounded by the  curves y²=4px and x²=4py

A: To find the area.

Q: Question 5 What is the limx→ [(ln(2x - 4)) - (ln(x+3))]? If your answer is a Whole Number Fraction…

A: limx-infinity [ln(2x-4)-ln(x+3)].

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Q: √=x if x1 Let f(x)=₂x

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Q: 11. f(sinx+x) dx

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: Solve the I.V.P using [x = zry]. y di dx + (y cos ( 1 ) - x) dy = 0, y (0) = 262

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Q: 2. f(x) = 4x5 + 3x² - 7

A: To discuss the continuity of the given function. To give the intervals in which he function is…

Q: Find the equation(s) of the tangent line(s) to the graph of the curve y-x-12x through the point (1,…

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Q: 12. DETAILS ZILLDIFFEQMODAP11 1.R.001. Fill in the blank. The symbol C₁ represents a constant. d =…

A: The solution is given below.

Q: да Given zTan¯¹ (x + y) — ln [1 + (x + y)²] = 5%, what is ду -1 2-2x-2y none of the choices 2- 2x +…

A: ∂∂xtan-1x=11+x2 Note : As per our Guidelines , we can solve first question. Please repost remaining…

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

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Q: Question 13 Given: ez + xy = 1 dz Find: dr zey te O dz 8x 8x dz 8x Za zerx Ty IZ ce¹² ze Ty

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Q: Solve the given differential equation by separation of variables. y In x dx x dx = (x + 1)² 12/2+2 =…

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Q: Find the area bounded by f(x)=x2-3x + 7 and g(x) = 2x + 7. (Round answer to two decimal places.) O…

A: Given equations, y=x2-3x+7y=2x+7We need to find point of intersectionx2-3x+7=2x+7x2-5x=0x(x-5)=0x=0…

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A: Solve the following

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A: