Find the equation of the plane containing the points (0, 1, 3), (2, 2, 2) and (3, 2, 1)

Q: Use double integration to find the volume of the solid on the first octant enclosed by the curves x²…

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Q: Je(ye-1) dr+e dy, where C' is the semicircle through (0, -10), (10,0), and (0, 10). (Compare Problem…

A: Using green theorem, value is evaluated.

Q: E = 5 -2 -4 3 2 2 -4 -4 -4 0 -3 2 3 2 4 4 -2

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Q: Find the general and Singular Solution of the Following differential equation y²Lny = xyP+ P²

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Q: Consider the general solution of a differential equation is y=C₁x-C₂ ln x² find C₁ and C₂ when…

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Q: B. Find the derivative of each of the following functions. - 3 15. f(x) = x² = ³ 2x - 1 16. x² -5x +…

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Q: 4. If 6.5 m³ of oil weighs 46,800 N, calculate its density in kg/m³. (a) 285 (b) 258 (c) 82 (d) 734…

A: Given problem:- 4. If 6.5 m³ of oil weighs 46,800 N, calculate its density in kg/m³. (a) 285 (b) 258…

Q: Evaluate the integral √ (k+ 2) ( k + 3) dx

A: Note:- according to the company policy we can attempt only one question so please upload the next…

Q: Use the chain rule to find where st the pieces: z = x²y + xy², x=3-t³, y=3-t6

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Q: With a curve 56 3 17 x² + y = 6, y = x, y = -2 and x = -2. . Determine its area.

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Q: Find the average value of the function on the given interval. f(x)=√x+3; [1, 22] (Type an integer or…

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Q: tan x 4. f dx csc x sec (In x)dx 5. X dx 6. f 1- cos 2x

A: I have stated the used formulas in the solution

Q: 5. Find the Maclaurin Series for f(x) = e²^²+ex 2

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Q: Find the average value of the function on the given interval. f(x)=x²-7: [0, 1] Set up the integral…

A: Average value of a function f(x) on [a,b] is given by, V=1b-a∫abf(x)dx

Q: Answer correctly, comprehensively, and neatly. Thank you. A vertical liquid storage tank shaped like…

A: A vertical liquid storage tank shaped like a cone has a radius of 8 m at the top and 22 m high.…

Q: Find I must find the indefinite integral then I need to use the result to calculate the definite…

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Q: Find two numbers whose difference is 128 and whose product is a minimum. X (smaller number) 64 64…

A: Given :difference of two number is 128

Q: Evaluate the following integral. JJ. xyz dV if S is the region bounded by the cylinders x² + y² =…

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Q: Given f(x,y) = 6x^2 - 2x^3 + 3y^2 + 6xy. Determine any local maxima, local minima, and saddle…

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Q: Find derivative of each; A) m(t)= In(4t^3+tan(5t)) B) h(x)= 4sin^8(5x+1)

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Q: reply as soon as posible.

A: To find out the conservative.

Q: 4. A spherical balloon is to be deflated so that its radius decreases at a constant rate of 15…

A: Using derivative

Q: 8 9 - 4e²™ dx Please approach doing this integral by hand with the following steps: First, make a…

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Q: Find the area of are a the region i) Sketch the ii) Determine the boundarien iii.) set-up the…

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Q: Given I(0) = cos (0 + π), (a) Find I(-) analytically. (b) Find I' numerically by using a central…

A: Given: Iθ=cosθ+π. (a) Differentiate with respect to θ, I'θ=-sinθ+π…

Q: The population of a city is 150,000. The city declines continuously by 4% per year. ... If this…

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Q: Compute the effective rate of interest corresponding to a nominal rate of 4.8% compounded…

A: We need to use effective interest formula.

Q: 1. Evaluate 2. Evaluate sin(20) 30 x-2x cos x sin x limo lim, 0

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Q: Find the derivative of each of the following functions. -6 8. f(x) = x +4x¹ 9. f(x) = 4x² +5x²³ 10.…

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Q: dy √y+4-2 5. S

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Q: 5. [7.6] If vectors ū=(5,2,-1) and = (2,-1, 3) then... a) determine u x v. b) Explain the geometric…

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Q: 3/7 Identify the coordinates of any local and absolute extreme points and inflection points. Graph…

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Q: A cylindrical can without a lid is to be constructed to contain 800 ml of liquid. Determine the…

A: To find the dimensions that minimize the amount of metal needed to make the can.

Q: Find the linearization f(x) = √x, L(x) = L(x) of the function at a. a=4

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Q: (a) For a certain curve, y"=2. Find its equation given that it passes through P(2, 6) with slope 10.…

A: Note: according to the company policy we can attempt only one question so please upload the next…

Q: A real estate firm estimates that the value of a certain property will be given by the function V…

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Q: x = 1. 2. Find the derivative of f(x) = 3x² - 5x at x = 1 using the formula f'(x) = lim f(x)-f(xo)…

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Q: Find the volume of the solid generated by revolving the region bounded by the lines and curves y =…

A: follow next step

Q: onvert the point p = (2,7) in the polar coordinate system to its artesian coordinate equivalent, and…

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Q: A particle moves along a straight line from the origin (at t=0) with the given velocity v. Find the…

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Q: Evaluate the double integral: To L 0 y x7 +1 y¹/3 x7 dx dy.

A: The given integral is: I=∫08∫y132yx7+1dxdy   So, The limit of the x varies from y13 to 2. The limit…

Q: Solve the differential equations i 4. y' + (tan x) y = cos²x, 8. e² y' + 2e² y = 2x

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Q: 3. Find f'(z) and f"(x) if f(x) = lnx + 2 cos³ r.

A: topic- derivative of a function

Q: Approximate the area beneath y = sin x on the interval [o, π] using the Trapezoidal Rule with n = 4…

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Q: cos(B) = −³, π< ß < 2π.

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Q: Use triple integration in Cartesian coordinates to find the volume of the region in the first octant…

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Q: Exercise 25.7.1. Give the Taylor series of the function 1 f(x):= 3x² around the point c = 1 and give…

A: The function is given by, f(x)=13x2 = 13x-2    ⇒f(1)= 13Differentiating the function 1, 2 , 3 ...…

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A: We will solve the problem

Q: Find an equation of the hyperbola with vertices at (±5, 0) and foci (±10, 0)

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Q: After t months on the job, a postal worker can sort L(t) = 700 – 400e−0.5ť letters per hour.…

A: answer is in next step .