1. Using Lagrange multipliers, find three positive numbers whose sum is 18 and such that the sum of their squares is as small as possible. Give the sum of the squares.

Q: 1 Use a limit comparison to test the convergence of |n+1 n=1

A: Given series ∑n=1∞1n+1 Recall limit comparison test

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

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Q: Show that the lines L1 : x =1– t, y = 2t, z = 4+t and L2 : x = 1+ 3t, y= 3 – 6t, z = 5 – 3t are…

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Q: 1. Given: - 4r? with f'(x) = (x+2)2 (r+8)(r - 2) (x+2)3 8(7r-4) (r+2)4 f(r) = and f"(x) = %3D %3D…

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Q: The reverse order of f, S, sin y² dydx is f, S sin y? dxdy False True

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Q: n: - 4.r? with f'(x) = (x+ 2)2 r(r+8)(r – 2) (x + 2)3 8(7.r – 4) - f(r) = and f"(x) = %3D %3D %3D…

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Q: 4. dx + (x – y + 2)²dy = 0

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Q: Calculate the Taylor polynomials T2(x) and T3(x) centered at x = 0 for f(x) = sin(x). (Use symbolic…

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Q: 4x2 8(7x – 4) x(x+ 8)(x – 2) (x + 2)³ - f(r) = with f'(x) = and f"(x) = %3D (x + 2)2 (x + 2)4 a.…

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Q: ences have the following generating

A: We have to choose the correct options from the given options according to the given information

Q: (2x – 3y +1)dx – (3x + 2y – 4)dy = 0

A: The differential equation Mdx+Ndy=0 is said to be exact, if ∂M∂y=∂N∂x. The solution of the…

Q: 2. Evaluate the following limits. 1-cos2z g. lim- 4z

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Q: 2(n!)2 (2n)! n=1

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Q: 12. Solve the following initial value problem: dy =3 dz VE-1 sin(y)' v(1) = 0. Make sure you write…

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Q: A projectile is shot from a cannon. The fixed parameters are the acceleratilon of gravity, g=…

A: We need to find time and approximation.

Q: Ray OB is the bisector of ∠AOC. The measure of ∠AOC = 7x+2 degrees and ∠ COB = 5x – 8…

A: A detailed solution is given below

Q: Determine the sum of the series п(п + 2) n= if possible. (If the series diverges, enter 'infinity',…

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Q: 1. The demand function for an electronics company's stereos is D(g) = 228.4 -18q and the supply…

A: Given problem:- 1. The demand function for an electronics company's stereos is D(q) = 228.4-18q and…

Q: diong the X-dXIS WiLII all dll and t is in seconds. If you know that the initial velocity is 6 m/sec…

A: According to our company's guidelines I can only answer first three subparts of the question. For…

Q: DIFFERENTIAL EQUATIONS Solve the following application problems. *show the every details of your…

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Q: уз dy S 1+9y2 3.

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Q: Find what is missing with complete solution

A: We know that ∫dx=x+c1. So,                 4∫dx=4x+4c1Let C=4c1.⇒4∫dx=4x+C

Q: 18. Determine if the equations are exact or not then solve for the general solution. a. (e*(x²y² +…

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Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

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Q: 4. dx + (x – y + 2)?dy = 0

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Q: Question Use the First Derivative Test to find the location of all local extrema for the function…

A: Given problem:- Use the First Derivative Test to find the location of all local extrema for the…

Q: Find a formula for the nth partial sum of the series and use it to find the series' sum if the…

A: The given series, 91.2+92.3+93.4+......+9nn+1+.......

Q: In the integration ; what integration method is appropriate? (3x-2)dx x+2r+17 a. Integration by…

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Q: I. Solve the following problems. af 1. Find af and of the function f(x, y) = arccot (-) + In ( ду…

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Q: ind equations of the following. 2(x- 8)2 + (y- 4)2 + (2 - 7)2 - 10, (9, 6, 9)

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Q: 5 In(3x) dx 5ln (3x) +C 12. 4

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Q: Find the vector component of v = 2i – j+ 3k along b = 2i + 4j + 4k and the vector component of v…

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Q: Use the Mean Value Theorem to show that f(r) = 2x sinh(x – 1) + 2" – x %3D has a critical number…

A: Given: We can see that the function is continuous in [0, 1] and differentiable in (0, 1). So, the…

Q: Question A tank is shaped like an upside-down square pyramid, with base of 2 m by 2 m and a height…

A: The volume of square pyramid with side of base a and height h is given by, V=13a2h At any height the…

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

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Q: Sin 26 de 9 sinte+4

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Q: Use the integral test to determine whet 2n n2 + 4 n=1 O converges O diverges

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Q: y² = x y = x³

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Q: 13. Obtain the differential equation of the family of straight lines at a fixed distance p from

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Q: dv v2

A: Use the basic properties of integration.

Q: Remember that rectangular form is z = a + bi and that polar form is z = r(cos 0 + i sin 0) Take…

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Q: Listen Use the Ratio Test to determine if the series converges or diverges. ne-Sn n=1 Converges…

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Q: Use vectors to find the lengths of the diagonals of the parallelogram that has i + j and i – 6j as…

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Q: Find the vector component of v = 2i – j+ 3k along b = i + 4j + 8k and the vector component of v…

A: Vector

Q: Let g be a function that is defined for all x, x # 2, such that g(3) = 4 and the derivative of g is…

A: Here, g(3)=4 & g'(x)=x2-16x-2, x≠2

Q: Now, let f"(x) =0 and solve for x. Remember that f"(x) = - sin is a periodic function, and thus…

A: use the equation above for solving the equation for x.

Q: Approximate the critical numbers of the function on the open interval shown in at each critical…

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Q: Solve the following and show the complete solution. 2. Using Lagrange multipliers, find three…

A: Let x, y and z be the three positive number so,  sum of number   x+y+z=18

Q: Solve the following and show the complete solution. 1. Find Duf at P: f(x,y) = sin(8x – 5y); P…

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Q: Find the gradient of the function at the given point. In(x2 – y) – 9, (3, 8) z = Vz(3, 8) =

A: use partial derivative for finding the gradient.