Use Lagrange multipliers to find a relative minimum function value of fif f(x,y,z)= x² + y²+ z² with the two constraints x +y + 2z = 1 and 3x - 2y + z = -4.

Q: y = 2x-3 2 x² + 4

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Q: Use Lagrange multipliers to find the critical points and the relative extrema. f(x,y) = 4x² + 2y² +…

A: We have to find  the critical points and the relative extrema.

Q: In a laboratory experiment, the population P of a microorganism is found to satisfy the differential…

A: The given problem is solved below in detail.

Q: 3. Convert the following polar coordinates to rectangular coordinates. 7π b. C. a. -3,- 2. 2…

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Q: A plane flies at a speed 580 km/hr at a constant height of 12 km. How rapidly is the angle of…

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Q: D. Graph each of the given functions and solve for the area of the region that they enclose. 2. 4.…

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Q: hello! Just a question, how are you sure that the given radius (2m) is on the top, not the base?…

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Q: A circular swimming pool full of water has a diameter of 24 ft and the sides are 5 ft high. Set-up…

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Q: a.) [ sec²(t − 1) dt b.) 2 √t c.) [ sin(Int)

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Q: Find Laplace Transform for 1-f(t) = 2t³; 2-f(t)=3e-²¹. 4-f(t)=2 cos(3t). 3– f(t)=sinh(2t); 5-cosh…

A: We have to solve given Questions.

Q: 1. Consider a point in Cartesian coordinates given by (3√3, -3, -8). (a) Find a corresponding…

A: Given that Cartesian coordinates (x,y,z)=(3sqrt(3),-3,-8).

Q: (x) = x² tan 3x+cot 3x

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

Q: If v= = (x² + y² +2²), then 925 + 02 +223 is 1 -1 -1/2 O Other:

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Q: Consider the region on the 1st quadrant bounded by y = √4x²,x and y-axes. If the region is revolved…

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Q: II. INDETERMINATE FORMS COS X X 5. lim x →∞0

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Q: Hwy find the integration 3 Se vadv V 1-

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Q: Find the solution of y" − 8y' + 16y = 0, y(0) = 1 and y'(0) = 5. y(t) = Ae4t + Be-4t y(t) = e4t+te4t…

A: The given equation is;  y''-8y'+16y=0, y(0)=1 and y'(0)=5.

Q: Find a Maclaurin series for f(x) = x2 e–x giving the first four nonzero terms and the general term.

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Q: In the partial fraction decomposition for some numbers A, B, and C. Find the value of B? -x²-x+2 C A…

A: On solving this we will get:  B= 1/2

Q: 3. Complete the table of values below. Then, sketch the graph of r = 2 - 3 cos in polar coordinate…

A: given isr=2-3cosθ

Q: Given the partial decomposition of the rational function for some numbers A, B and C. What is the…

A: Given :x+1(x-1)(x-2)(x+3)=Ax-1+Bx-2+Cx+3

Q: 1 √3 5) 2 2 / 9) (-1,0) 7) 3√3 3 2 2/3 " 2 ।

A: Topic = Geometry

Q: If $200 f(x) dx = A and 200 f(x) dx = B, then 130 f(x) dx =? 50 130 A+B B-A 0 O A-B

A: Given: ∫50200f(x)dx=A and ∫130200f(x)dx=B Now, we know: ∫abf(x)dx=∫acf(x)dx+∫cbf(x)dx Using above…

Q: Find Vf at the given point. f(x,y,z) = x² + y² -32² + z lnx, (1,4,5) Vf|(1,4,5) = 7i+ (8)j + (-30)k…

A: Topic = Derivative

Q: Consider the region on the 1st quadrant bounded by y = √4x²,x and y- axes. If the region is revolved…

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Q: Find the following improper integrals a) dr b) fodr

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Q: The value of x for which the series A. 2<x<3 or 3<x<4. B. x<2 or 4<x. C. 2<x<3 or 3<x ≤ 4. D. 2<x<4.…

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Q: The area between the curves f(x) = x and g(x)= x^2 on interval [0.2] * 02 Me: wow I finally…

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Q: An aircraft sets a course with a certain bearing and at a speed of 500 mph. A horizontal wind…

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Q: Let R be the region bounded by the functions f(x) = 4x² + 6x and g(x) = -2x² - 6x as shown in the…

A: Given f(x)=4x2+6x, g(x)=2x2-6x Here point  intersection of f(x) and g(x) is x=-2 and x=0 Therefore…

Q: A rope that weighs 0.5 lb/ft is attached to a bucket filled with cement plaster that weighs 22 lbs.…

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Q: f(x) = 4x² 8x +3 - x²+x-12

A: The given function is f(x)=4x2-8x+3x2+x-12

Q: if the function u= ln (x^3+x^2y-y^3/x-y) then x su/sx + y su/sy is

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Q: * (ارفق الاجابة) The eigen value of matrix 1 -1 O 1+i, 1-i O 1+i, 1+i O 1,-1 11 1-i, 1-i

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Q: How many arbitrary constants can be obtained from the answer if the given y"+y'+6y=9x³+x²-x is…

A: We know, The number of arbitrary constants in the general solution of a differential equation is…

Q: I the function z(x, y) = ex sin(3y) and x = ut-t², y = √u² + t², Find : dz dz and 2- (by chain rule)…

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Q: A spherical snowball is melting in such a way that its radius is decreasing at rate of 0.1 cm/min.…

A: V=4πr3/3 dr/dt = 0.1 cm/min dV/dt =?   dV/dt = 4πr2(dr/dt)   dV/dt = 4(3.14)(9)2(0.1) dV/dt = 101.73…

Q: 6. In(x³y²) = x² +y³

A: Let's find second derivative of given function.

Q: 2 - Find the average value of the function f(x)=x -21 on [0,6]. The average value of the function…

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Q: What is y2 = 3x in polar form? r = 3 sin 0 sin 0 O Option 4 r = 3 csc 0 cote Option 2 r = 3 sin 0 -…

A: Given y2=3xTo find polar form:

Q: Evaluate the limit using L'Hopital's rule. Answer should be expressed as an INTEGER value, with NO…

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Q: Answer and give the complete solution. The lower edge of a mural, 12 ft high, is 6 ft above an…

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Q: x4 dx 2 2 (x² +9) ² 3 = 3 WIX 2 Arctan là + 51]+c 4 (x249)

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Q: Evaluate the limit using L'Hopital's rule. Answer should be expressed as a numerical value, with TWO…

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Q: What is the graph of r cos 0 + r sin 0 = 1? Oline with slope m-1 and intercept b=0 Oline with slope…

A: We know that x = rcos(theta) and y = rsin(theta)

Q: Find the solution of the following initial value problem d2y/dx2 + 2 dy/dx − 3y = 12ex ,  y = 0 and…

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Q: Determine the graph of g = x^2 + sqrt of (x + 1) and solve for its extrema, concavity, and points of…

A: Please see the below picture for detailed solution.

Q: find the limit as x approaches to infinity (x-3 / x+1)^x/a

A: We need to evaluate the value of the following limit limx→∞x-3x+1xa Formula Used:  limx→∞1+mxx = em…

Q: Sketch out the graph of ? = ?^2 + sqrt of ? + 1, and find its extrema, concavity, and points of…

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Q: Let F and G be vector-valued functions such that F(1) = (1,0, 2), Ģ(1) = (2,1,3), Find (Go ƒ)'(0) +…

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