5-Given n+1 data pairs, a unique polynomial of degree.........passes through n +1 data point. a-n +1 b- n c- n or less d- n +1 or less

Q: using Polar tics II, e the card Find the Q3) By using the polar find region enclosed by y = x² and y…

A: To use polar coordinates to find the region enclosed by the below equations. y=x2y=1

Q: Q1/ find the Eigen value and Eigen vector for the smallest Eigen value if [2 1 -11 [A] 3 2 -3 L3 1…

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

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Q: 2. You have a fair five-sided dic. The sides of the die are numbered from 1 to 5. Each die roll is…

A: Please see the attachment

Q: Find the particular solution to the differential equation: 2(y')² ( y" = 1- when +3) x = 0, y = 1…

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Q: 1 Show that IS the separable me tre space (R, d), where el(x, y) = be-y/

A: Here we use basic real analysis

Q: Solve: y''y' 6y = - 12t + 28 - y(0) = -6, y'(0) 21 y(t) =

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Q: after t seconds. A particle undergoing straight line motion has velocity v = (t²+1)² where the…

A: given velocity of the particle v=4tt2+12 where 't' is in seconds

Q: OS: S ≤²≤ √√4-(2₂²2. that lies above th sing spherical coor

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: The fish and game department in a certain state is planning to issue hunting permits to control the…

A: Given statement, The fish and game department in a certain state is planning to issue hunting…

Q: Consider the result (1.d) above. We will use it to calculate the solution for the ODE ƒ"(t) + ƒ' (t)…

A: As per the question we are given a second order non-homogeneous differential equation as : f''(t) +…

Q: et(1 + cos(3t))

A: Let us write the mathematical expression to a MATLAB expression in the next step.

Q: (9) 2z+p²+qy+2y² =( z = ax 2 2 +²²2 + -2 + C₂

A: Let us consider the PDE F(x,y,z,p,q)=0 The charpits formula…

Q: (b) In the figure, AOC and BOE are straight lines. Angle A and angle B are equal. ED is equal to CD.…

A: Given: In the following figure, AOC and BOE are straight lines. Angle A and B are equal. ED is equal…

Q: 2. Given the values for f(x) on the table, approximate the area under the graph of f(x) from x = -5…

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Q: e work of a particle moving counter-clockwise around the vertices (2,0), (-2,0) and -3) 3e* F…

A: Greens theorem is used

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

A: Solution :-  Given :- Vertices = 10  Because we know that,Tree with n vertices which means n−1…

Q: Use mathematical induction to prove that for all integers n ≥ 1, 1 +7 +13 + 19 + ... + (6n − 5) =…

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Q: Consider the paraboloid paremterized by o(u, v) = (u, v, u² + v²). 1. Find the second fundamental…

A: 1 Consider the paraboloid parameterized by σu,v=u,v,u2+v2. We have to find the second fundamental…

Q: (b) Find the singular solution of дz where p = and q ax = z = px +qy+p² +q² + pq, дz ду

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Q: Solve the following equation using bisection method to find the root between x₁=1 and x2=5, make 5…

A: We have to solve the following equation using bisection method to find the root between x1 =1 and x2…

Q: Q5/ Use double integration in Polar coordinates to find the shaded area in figure (the area inside…

A: The area is A=2∫π6π4∫2 cosθ2 sin2θr dr dθ We now evaluate this: A=2∫π6π4∫2 cosθ2 sin2θr dr…

Q: D. Suppose p, q, r, s are propositions such that p^q is true and rv sis false. Determine the truth…

A: We know that,  A∧B is true if and only if both A and B true  A∨B is false if and only if both A and…

Q: Q8) Use cylindrical coordinates to find the volume of a curved wedge cut out from a cylinder (x -…

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Q: How many strings of length two can be formed by using the letters A, B, C, D E and F without…

A: Given letters, A, B, C, D, E, F We have to find number of strings of length two

Q: (b) Solve for the partial differential equation a²u 1 a²u c² at ² u(0,t)= u(1,t)=0 u(x,0)=2x and dx²…

A: Given partial differential equation is ∂2u∂x2=1c2∂2u∂t2, u0,t=u1,t=0, ux,0=2x and ∂ux,0∂t=10. We…

Q: pigeonhole principle guara e a streak of at least I losing

A: Given as, number of lottery tickets = 100 according to question, number of winning tickets = 12 the…

Q: 5. Every single card is used to represent each letter of the English alphabet, which is then placed…

A: Given, Every single card is used to represent each letter of the English alphabet, which is then…

Q: Calculate the Laplace transform of: a. f(t) = t sinh (at) b. f(t)=1²e-t c. f(0) = √i

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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: 2x + 6y = 4 5x + 15y = 10 Use the substitution method and show work.

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Q: • Find the upper Riemann sum U(f, P) and the lower Riemann sum L(f, P) for each of the following…

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Q: Consider the function v(x, t) that satisfies the PDE vx + 8xvt=0 for x>0 and t> 0, and the initial…

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Q: All statements below are false. Provide a counterexample of f and g each. (a) If f + g and fg are…

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Q: Let D = R² and f:D → R that f₁ (partial derivative off with respect to the 1st coordinate) and £2…

A: As per the question we are given a region D on the plane R2 and a function f from D to R , such that…

Q: VI. Find (a) Fourier Cosine Series (b) Fourier sine Series of the following using Half-Range…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

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

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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: Es, given that x(0) = -1, and y(0) = 0 *+x+2y-1=0 2x+y+y-2=0

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Q: Use Stokes theorem to evaluate ff.curl F.nds. where F = (xyz, x, e* cos z), while S is surface x² +…

A: Solution :

Q: A cylindrical can of height h and radius r is to be made with a fixed volume V. Show that the area…

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Q: Car Evaluate the integral a(z-a)"dz = where Car denote the circle of radius 0 if n = -1 (2πi if n =…

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Q: Given the polynomial :x6y³ - 2x²y² + 1 1. What is the degree of the first term? 2. What is the…

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

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Q: Exercise (1-3): By Charpit method solve the following PDE Question Answer (1) p²x+q²y=z z =…

A: We have to solve the given problem.

Q: (a) Let R be a ring and S a subset of R. What does it mean to say that S is a subring of R?

A: a. S is a subset of R. A non-empty subset S of R is a subring if a, b ∈ S ⇒ a - b, ab ∈ S. A subring…

Q: Q5: (A) If the matrix A = [3 5 7; 10 11 12; 2 4 6; 13 14 15], find (5 only) ( 1. A([2 3],[21]) 2. A…

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Q: [8] Find the complex Fourier integral representation of f(x) = e2x 0 |x| < 1, |x ≥ 1.

A: The given problem is to find the complex Fourier integral representation of the given function.

Q: 1. Start with an unknown number. Triple it and then subtract 5. Now, take the new number and double…

A: Let the unknown number be x. We have to triple it and subtract 5 from it . This is 3x-5. Take this…

Q: the volume of the solid B that lies above the cone z = √√x² + y² and below the sphere x² + y² + z² =…

A: We will use relation between cartesian and spherical co ordinate to set up triple integral for…