Find three positive integers x, y, and z that satisfy the given conditions. The sum is 33, and the sum of the squares is a minimum.    (x, y, z) =

Q: I. Solve the following integrals using Algebraic Substitution 1. ſ 2. S -1dx dy y+4-2

A: ∫un du = un+1n+1+C ∫1au+b du =1alnau+b+C ∫1u2+1du = tan-1u+C

Q: Use Simpson's rule with four subdivisions, to estimate the following integral f/² cos x dx

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Q: y= 2x³-27 3x4 - 2x Find dy da

A: Given: y=2x5-x33x4-2xTo Find: To find dydx.

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A: Find the volume of parallelepiped

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Q: Given z = f(x, y), x= x(u, v), y = y(u, v), with x(4, 2) = 5 and y(4,2)= 1, calculate zu(4, 2) in…

A: Given that z = f(x,y) , x =x(u,v) , y=y(u,v)  we have to find zu(4,2)

Q: Evaluate the following limit or explain why it does not exist. 6 X lim (1+7x) X-0 Select the correct…

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Q: Determine any planes that are parallel or identical. (Select all that apply.) P₁: -90x + 120y + 60z…

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Q: For this problem, you will use the following equation in your calculations, where f(t₁) = a, a > 0,…

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Q: If z=5x^2+y^2 and (x,y) changes from (1,2) to (1.05,2.1), compare the values of delta z and dz.

A: Given that        z=5x2+y2 changes from (1,2) to (1.05,2.1)  We have to derive value of Δz and dz .…

Q: Given f(6)=3, f′(6)=11, g(6)=−1, and g′(6)=7, find the values of the following (a) (fg)′(6)= (b)…

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Q: A bag contains three red marbles, three green ones, one lavender one, two yellows, and three orange…

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Q: Find the component form of u + v given the lengths of u and v and the angles that u and v make with…

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Q: Prove that the graph of the function y = x² −3+1/x has at least two x-intercepts in (0,2).

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Q: r- 24. y" +9y = 0; y(0) 25. y"-2y' + 2y = 0; 26. y" - 2y' + y = 0; 27. y"" - 4y" + 7y' - 6y=0; = 1,…

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Q: The indicated function y(x) is a solution of the given differential equation. Use reduction of order…

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Q: Find the volume of the solid generated by revolving the region bounded by the curve y = In x, the…

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Q: Find the directional derivative of the function at P in the direction of v. == P(1, 2), v = -j f(x,…

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Q: Evaluate the following integral: Sºa dx -00x²+1

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Q: roo dx X² O

A: We will find the given integral.

Q: 4. Solve y 3x 3y + 2y" e using undetermined coefficient. Show all the work.

A: We need to solve D.E.

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Q: The indicated function y(x) is a solution of the associated homogeneous equation. Use the method of…

A: The given equation is;  y''-3y'+2y=5e3x.

Q: Use a triple integral to find the volume of the solid bounded by the parabolic cylinder y = 6x² and…

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Q: 3 y = (₁ ² +1) ² Gi Find 13y dx²

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Q: Find a linear differential operator that annihilates the given function. (Use D for the differential…

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Q: Find an equation of the plane with the given characteristics. The plane passes through the points…

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Q: Write the given differential equation in the form L(y) = g(x), where L is a linear differential…

A: We have to find solutions

Q: 1 (2+√3)

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Q: =4 Sin4n 3n A. The limit of the sequence is: B. The sequence diverges.

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Q: Solve the following by indicating the steps and describe the process: sinx dx SCOS² 1.

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

Q: z = cos(x² + y²), nd Əz/əu and Əz/av. The variables are restricted to domains on which the functions…

A: Use chair rule.

Q: Find k, given f(x, y) = k(y² + xy) and [ [ f(x, y) dxdy = 54 R R=0 < x < y < 2

A: Given problem:- Find k, given f(x, y) = k(y² + xy)  And ∫∫R f(x, y) dx dy=54 where R…

Q: Evaluate f xdx (x²+1)²

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Q: Find the following derivatives. Express your answer in terms of the independent variables. 2x - 2z…

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Q: Problem 2.3 Evaluate 2x² + 3x + 1 2x - 3 lim x-1 x².

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Q: Find two unit vectors in 2-space that make an angle of 45° with 8i + 5j. 1 I NOTE: Enter the exact…

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Q: es The bearing of a ship from a lighthouse was found to be N 16° E. After the ship sailed 7.3 miles…

A: This question is based on use of Sine law.

Q: Use the integration capabilities of a graphing utility to approximate to two decimal places the area…

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Q: Consider the following functions. f₁(x) = 0, f₂(x) = x, f(x) = ex g(x) = C₁f₁(x) + C₂f₂(x) + C₂f3(x)…

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Q: Determine whether the given differential equation is exact. If it is exact, solve it. (If it is not…

A: Explanation of the answer is as follows

Q: a drug is injected into the bloodstream of a patient through the right arm, the drug ntration in the…

A: Topic:- application of derivatives

Q: e Determine the equation of the tangent line to y=x2(√x+x la a C C C C C C C

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Q: 5. Find the 6th term of the recursive sequence defined by a₁ = 0, an+1=2a₁ +3.

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Q: Find the domain of the function f(x) domain? = 1 √ x² + 1x 30 . What is the greatest value of a not…

A: The given function,  fx=1x2+x-30

Q: A ball sits on the point (1,1) and touches the f(x,y)=5-(x^2+y^2). In which direction graph of will…

A: Here is the solution of the given problem.

Q: Show that y=sec^2x and y=tan^2x have the same derivative. What can you say about y=sec^2x-cot^2x?

A: Given y=sec²x and y=tan²x Now derivative dy/dx=d/dx( sec²x) =d/dx(1+tan²x) dy/dx= 2tanx sec²x   Now…

Q: Find the general solution of the given higher-order differential equation. y""+ 2y" 16y'- 32y = 0…

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Q: Use the fact that the volume of a tetrahedron with adjacent edges given 1 by the vectors u, v and w…

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