Q5/ Use double integration in Polar coordinates to find the shaded area in figure (the area inside the rose r = 2 sin(20) and outside the circles r = 2 sin(0) and r = 2 cos (0)). r-2 sin(0) Ans/ A = sin20 2 J 4 = 2√² r dr de then continue... 2 cose 4.5 -2 sin(20) -2 cos(0) 2.5

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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: 55² +25-4 (5+₁) (S+₂) (S+ 3) Taking Laplace transform

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Q: Let M, be the additive group of all nxn matrices with real entries, and let R be the additive group…

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

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

Q: Function 1 2 x +1 on the interval (-3,3) and has n=5. Evaluate the function using integration.

A: We will use basic integration.

Q: Obtain the solution of the following differential equation y"-4xy' +(4x² - 2)y = 0

A: We have to find solution of given differential equation  y''- 4xy' + (4x2 -2)y = 0

Q: Q5(a) Let f(x) be a periodic function with period 4 such that f(x) = {2; 0<x<2 2<x<4 (1) Find the…

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Q: Q4: Let X be a discrete random variable with probability mass function given in the following table:…

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Q: How many positive integers less than 1,000,000 have a digit sum of 5

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Q: coordinates with dV= r dz d 4-(x2 + y2). Draw the solid

A: Using the volume of cylinder and the solid is given as,

Q: Let R be the region in the first, third, and fourth quadrants that is inside the polar curve r = 1 -…

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Q: By direct partial integration, Solve the following PDES 8- X 8²Z 5 4 dz z(x,0) =X+X, Z (2,y) = 3 y z…

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Q: ) Find the result of the following equation: A = 3² + 3+3² √2

A: To find the result of the given equation :-

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: [R Evaluate L S²+5-2 (S+2) (8-5) ²

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Q: 3 By direct partial integration, Solve the following PDES 8- X²Z ахду 4 JZ = 0, Z(X₂0) = x² + x, Z…

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Q: INSTRUCTIONS: • Please write clearly and understandable way. Write all the corresponding Given with…

A: Please see the attachment

Q: 3. Dwight is selling baskets of beets. If the profit in selling a baskets is P(x) = 200x² 3 200x +…

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Q: 2. Let f I→ R be Riemann integrable on I = [a, b], a, b = R, a <b, and let F be an an- tiderivative…

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Q: By Separation of variables, Solve the followin PDES :- • Su d2u dx2 @ o dt U (0₂t) =(4,t) = o u…

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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: Use undetermined coefficients to find the particular solution to y'' + 5y' + 4y = 3e³t Y(t) =

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Q: Find Domain and Range Sove all points without leavin ℗ x + y² + Z 2 X+ 4+=+/-5 +2Z 3 Sin(x+3y) +2…

A: Domain is the set of points where function is defined. And range is set of images of function.

Q: The diagram shows the curve y = ex and the tangent drawn at x = 2. AY X

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Q: Evaluate the double integral that will find the volume of a solid bounded by z=1-2y²-3x² and the…

A: To find the volume of double integral that is bounded between z=1−2y2−3x2 and xy-plane.

Q: 3 By direct partial integration, Solve the following PDES 8- дги axdy. = cos x cosy x U(X₂#) = X…

A: Given ∂2u∂x∂y=cosxcosy, ∂∂xux,π=x, uπ,y=2cosy

Q: (b) Show that the continuous image of compact set is compact but the convers need not to be true.…

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Q: Q4\ Find the average value of f(x,y) = (+√y) where 0≤x≤y and 0 ≤ y ≤ 4.

A: We have to find the Average value of given function in given domain.

Q: b.S) suppose a pendulum with length L (meters) has angle (radians) from the vertical. It can be…

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Q: 2. A man put a pair of rabbits in a cage. During the first month the rabbits produced no offspring…

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Q: At 8 a.m., you place a certain amount of bacteria on a slide. Every hour, the area covered by the…

A: This is the problem of Modelling and differential equations.

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: Consider the differential equation " - 4y + 5y = f(t). such that y(0)=0 y y'(0)-2. The function f(t)…

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Q: 7) A can of soda with a temperature of 56 degrees Fahrenheit is placed in a refrigerator which is…

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Q: 2. A man put a pair of rabbits in a cage. During the first month the rabbits produced no offspring…

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Q: 3. Ronnie goes to the racetrack with his buddies on a weekly basis. One week he tripled his money,…

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

A: Given equation in different co-ordinates system. we have to convert them into cartesian co-ordinate.

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: 6 By separation of variables, Solve the following 5 PDES :- du dt = 2 d24 dx2 © o U (0₂t) =(4,t) U…

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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: Consider following definition of function. f: X→X, f(x)≡(3x+11) mod 26, where X={0,1,2,....25}.…

A: f(x) = (3x+11) (mod 11) X = {0, 1, 2, ..., 25} GCD(3,26)=1

Q: r² (t) = 2 + ₁ + (²² + 3)) + (2+² + 5) k 明 Find ICH and ÑA)

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Q: Use the Jacobi method to find approximate solutions to 3x110x2 - 4x3 = 9 20x1 + 2x2 + 3x3 = 25 2x12…

A: Don't confuse with the notation of variable . Here we use xk,yk,zk for approximate first ,second…

Q: Use the quadratic interpolation and the following data to find f(1.4) X 1 1.2 1.3 1.4 1.5 F(x) 0.368…

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Q: 2. A man put a pair of rabbits in a cage. During the first month the rabbits produced no offspring…

A: To find how many pairs of rabbits will there be at the end of the 5th month :-