Use Stokes' theorem to evaluate frotF. ds. F(x, y, z) = xyi + e²j + xy²k; S consists of the four sides of the pyramid with vertex (0,0,0), (0,0,1) and (0,1, 0) that are to the right of the xz plane, oriented in the direction of the positive y axis.

Q: C R using cylindrical c √1-2², 0≤ ≤ the solid B that lies +22=2 using sphe

A: 6. (a) The required solid is R=x,y,z: 0≤x≤1, 0≤y≤1-x2, 0≤z≤4-x2+y2. In cylindrical coordinate…

Q: X + y = 6 2x - y = 0 Solves using the substitution method

A: We need to solve the system of equations  x+y=62x-y=0 using substitution method

Q: Find the point wise limit of the sequence &{fn} the sequence {fr} Where Sin nx In (x) = √n if tay J…

A: Here we use basic limit property

Q: What is the negation of the proposition/statement: 10 > 14 ?   10 < 14   10 ≥ 14   10 ≤ 14   10…

A: Given, proposition/statement is 10 &gt; 14  We have to find negation of the given…

Q: of R using cylin S√1-², 05 of the solid B t 22 neir

A: 6. (a) The required solid is R=x,y,z: 0≤x≤1, 0≤y≤1-x2, 0≤z≤4-x2+y2. In cylindrical coordinate…

Q: Rusing cylind √1-2², 09 the solid B th +22=2 using

A: 6. (a) The required solid is R=x,y,z: 0≤x≤1, 0≤y≤1-x2, 0≤z≤4-x2+y2. In cylindrical coordinate…

Q: b) Find the area between the 2 curves f(x) = x² +4-4x and x- with the two lines = 5 &x= 2. axes and…

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Q: Consider the sequence 20, 14, 8, 2, ……, (a)    Write a recursive formula of the sequence (b)…

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Q: (c) f(x) = |x₁| + |x₂| for x = = (x1, x₂) € R².

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Q: 2) Given that the total flux across the surface, S of the tetrahedron bounded by the planes x = 0, y…

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Q: a. Find an explicit formula for the sequence 1,-4,9,-16, ... b. Determine the first four terms given…

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Q: Find a recurrence relation and initial conditions for the sequence 1, 4, 13, 40, 121, 364, ...

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Q: 5. Use Cartesian coordinates to evaluate Jff v² av where D is the tetrahedron in the first octant…

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Q: 5. Use Cartesian coordinates to evaluate JIS y² dv D where D is the tetrahedron in the first octant…

A: We have ∫∫∫D y2 dV D is tetrahedron in first octant bounded by coordinate planes and 2x+3y+z=6 So,…

Q: 3.6 Let A be a subset of a metric space (S, d). Show that if H is a nonempty open subset of S and An…

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Q: 3.1 Let S be the set of all bounded continuous functions f: [a,b] → R. Given two points f and g in…

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Q: Convert integers 205 and 12 to binary representations and find their product using the binary…

A: We have to convert the number 205 and 12 to binary representation and find their product using the…

Q: Q4) Prove that dx 1+ 2 sinx || In √3 Χ tan tan x + 2 -√√3 +2 + √√3

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Q: C-1 { e3pe-3p p²-4

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Q: if (11 + 2! = d+ie), find the equation of 1+ 21 the ellipse whose Vertex is the origin and the one…

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Q: Q3: Use Euler's Method to find a numerical solution of the differential equation dy y = 3 - dx X =…

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Q: 2. (a) How many lines of symmetry does a regular octagon have?

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Q: aluate

A: The limit of integration of the variable x varies from x=y13 to x=2. The limit of integration of the…

Q: You may find this question challenging. Given the three points A-[1,6], B-[-1, 1] and C= [4,6],…

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Q: sing cylindric -2²2², 0≤ solid B that 2 = 2 using s

A: 6. (a) The required solid is R=x,y,z: 0≤x≤1, 0≤y≤1-x2, 0≤z≤4-x2+y2. In cylindrical coordinate…

Q: [(x² - 2xy)dx + (x²y+3)dy ans: Verify Green's Theorem in plane for c of the region defined by y² =…

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Q: 1. Identify the surfaces of the following equations by converting them into equations in the…

A: This is a problem of change from spherical to cartesian and polar to cartesian.

Q: | (6) 22 = pqxy z = c.xyla ٥/۳

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Q: Use Cartesian coordinates to evaluate Jff ² av where D is the tetrahedron in the first octant…

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Q: The volume, Vm³, of liquid in a container is given by V = (3h² + 4) - 8, where h m is the depth of…

A: Given, V=(3h2+4)34-8 Where V m2 is the volume at any depth h m.

Q: Evaluate the double integral that will find the volume of a solid bounded by z = 1-2y²-3x2² and the…

A: We have to find the volume of the solid bounded by z=1−2y2−3x2 and the xy plane.The volume of the…

Q: Find the volume of the region in the first octant bounded by the coordinate planes, the plane y+z=8,…

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Q: Find the unique, closed form solution to this recurrence relation given the initial conditions: an =…

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Q: Q5: Use the quadratic interpolation and the following data to find f(1.4) X 1 1.2 1.3 F(x) 0.368…

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Q: Let M = {1, 2, 3, 4, 5, 6, 7, 8) and be cyclic permutations: f1 = (1, 2, 3, 4), f2 = (4, 5, 6), f3 =…

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Q: Bisection Method Equation: f(x)= x³ + 2x²+x-1 Tolerance: x10-5 Assume a = 0; b = 3

A: We have to solve the given problem.

Q: (c) The figure shows two similar prisms, if the volume of Prism I is 40 cm³, find the volume of…

A: Solution :-

Q: 1. Consider the differential equation: y" - 3y' + 7y = f(t), such that y(0) = 0 and y'(0) = 2. The…

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Q: Determine whether the Fourier series of the given function will include only sine terms, only cosine…

A: Given function with interval  fx=5-x3,  -4≤x≤4 where 2l=8⇒l=4

Q: Show that (2+x, e) is linearly independent. Plz solve both parts within 30-40 mins I'11 upvote your…

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Q: Q3: A Cummins diesel engine is available in heavy-duty pickup trucks. The probability of the engine…

A: Conditional probability  If two events A and B associated with a random experiment . Then the…

Q: [7] Find the complex Fourier series of f(x) = COS X 1 0≤x≤ π, -π < x < 0.

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Q: 6. Set up the triple integral that will give the following: (a) the volume of R using cylindrical…

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Q: Write an equation for the transformation of the parent function. 6 4 8 2 g(x) = -(x-4)³ + 2 O g(x) =…

A: As we can see that the red line represents the cubic function. So, from the graph, it has the parent…

Q: The number of computers sold per day at a local computer store, along with its corresponding…

A: X P(X) X.P(X) (X-μ) (X-μ)2 (X-μ)2.P(X) 0 0.1 0 -2.2 4.84 0.484 1 0.2 0.2 -1.2 1.44 0.288 2 0.3…

Q: b). Using an appropriate triple integral, evaluate the volume of: i). ii). z = V1 – x² - y² r = sin…

A: As per Company guidelines i am solving first question please resubmit the question for another one.…

Q: no of edges for a tree with number of vertices 10 is

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Q: Can you help me with this by showing all the steps. Thank you A gasoline station can sell 10,000…

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Q: Suppose that 100 lottery tickets are given out in sequence to the first 100 guests to arrive at a…

A: The final answer is l = 8

Q: 6. s] Set up only a triple integral that will give the following: (a) the volume of R using…

A: (a) Given,R:0≤x≤1 ,  0≤y≤1-x2 and 0≤z≤4-x2-y2 we know the relation between cylindrical and cartesian…