Show that for the Legendre polynomials Pn the following holds for all n E N (n+1) Pn+1(x) − (2n +1)xP(x) +nP₂−1(x) = (2n +1)Pn(x)

Q: ron whose edge measures 6 m

A: Given that the edge measure of a regular icosahedron is 6m.

Q: Prove that 197 is prime

A: In this question, prove that 197 is a prime number.

Q: n of parameters to find the general solution of the

A: Use the method of variation of parameters : The given differential equation is y''-2y'+y=et1+t2+3et…

Q: 12. If the x-term is missing, then the quadratic equation cannot be used.

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: Write the number 56 as a Mayan numeral

A:

Q: 1 (-1)-1 (ii) 1 +... 5 2n-1 (b) Show that the interval of convergence of the series 1 1 -√2ses.…

A:

Q: If the Laplace transform of a function ƒ is defined and denoted by F(p), find an expression for the…

A: The solution is given as

Q: Q4) Determine whether the series is convergent or divergent. 1 a)Sw=15 7n2-13n+9 nt+16 b)Σ=17…

A:

Q: Find where each of the following functions is discontinuous (a) tan(x) (b) cosec(x) (c) |x|

A: Solution a: Given function is y=tanx Since at π2 , tanx does not exist. Now, we will see it in graph…

Q: Let p>5 be a prime number prove that expression p^4-10p^2+9 is divisible by 1920.

A: A top wide variety is a herbal wide variety large than 1 that isn't always the made of lesser herbal…

Q: vergence for lim 6-0 sin h hº cos h h 0.

A: Given that limh→0sinh3-h3cosh2h=0. The rate of convergence can be calculated by evaluating the…

Q: The amount of time required to serve customer at a fast food restaurant has an exponential density…

A:

Q: 8 d. Sex 0 dx

A:

Q: 4. Let S = {a, b, c, d, e, f, g, h} and T = {b, c, d, f,i,j}. a) List the entries of the set S-T,…

A:

Q: Assume g(x,y) is a function of the form x³y g(x,y) = √²x²y³² ( O 1g (x, y)| ≤ lally! then < Show…

A: Solution ; g(x,y)=x3yx2+y2,(x,y)≠(0,0)0,(x,y)=(0,0) Use parametrization to prove required result,…

Q: Exercise 4J 1 In a town three schools A, B and C are located at the points with coordinates A(1, 3),…

A: Given that, A, B, C  are three school located at the points with coordinates A1,3, B6,4 and C6,1.…

Q: Check the differentiability of the function f(x, y) = √xy | at the point (0,0). Also check the…

A: As per the question we are give a bivariate function : f(x,y) = √|xy| And we have to check for its…

Q: Let A and B be non-empty sets. Using the element method prove that: If ACB, then AU (B - A) = B. You…

A: Given A and B be non-empty sets. We have to prove that if A⊆B then A∪B−A=B. Let x∈A∪B−A ⇒x∈A or…

Q: (a) Prove the convergence or divergence of each of the following series: 1! +a! +3! + +n! 20+1 2+1 6…

A: Disclaimer: Since you have asked multiple question, we will solve the first question for you. If you…

Q: Find the volume of the solid obtained by rotating the region bounde specified line. Sketch the…

A: Follow the steps.

Q: Consider the following equations Y₁ = 3x + 4 2y2 = 2x+8 -Y3= x-4 -3y4 = 9x - 12 What do the lines…

A: Given equations of lines are y1=3x+4             (1) 2y2=2x+8          (2) -y3=x-4            (3)…

Q: . A Garments Factory produces 2 kinds of curtains: Curtain A and Curtain B. For materials, the…

A:

Q: [[ (x + 1)" dx dy D

A:

Q: A sculpture is 9 meters tall and has a volume of 5,400 kilograms. An artist creates a

A: Introduction: A proportion is a term we use to describe a statement in which two ratios are equal.…

Q: Consider the points as shown in the table below, find fo.fi,f2 and f3 using three points formula. 0…

A: Solution: Apply 3 point formula to calculate differential. table for x and y x 0 0.25 0.5 0.75 1…

Q: Let R be the rectangular region defined by the following. R = What is the value of the following…

A: We have to find the value of the integral ∫∫R3 dS where R=0,1×0,2=x,y∈ℝ2| 0≤x≤1, 0≤y≤2

Q: A population of single-celled organisms was grown in a Petri dish over a period of 16 hours. The…

A: Given: Time (x) Number (y) 0 25 2 36 4 52 6 68 8 85 10 104 12 142 16 260 To…

Q: Solve the ordinary differential equation y'+4y-3x³, using Runge-Kutta method with Xe 0, Yo-1, X₂-2,…

A:

Q: 4) Find the volume of the solid bounded above by the graph of f(x,y)= xy³and below by the xy-plane…

A:

Q: The board of directors of SSS Inc., have de

A: Given that the board of directors of SSS Inc. has declared a dividend of P18,000,000. The company…

Q: 29,369 as the forec

A: Given data: weight on actual value of 0.34.

Q: 1. Based on the data, what is the mean nominal wage? A. 123.26 B. 291.81 C. 350.00 D. 358.88 2.…

A: Part (1) The nominal wages are: 537, 350, 340, 360, 400, 400, 320, 310, 395, 386, 315, 316, 365,…

Q: Prove or disprove the following statement: "For all real numbers x, y, [xy] = [x][y]." (3 marks)

A: Introduction: Two important functions are frequently used in mathematics and computer programming.…

Q: Use Leibnitz's Theorem to calculate the 4th derivative of y = x^sin (3x)

A:

Q: x ²" (t) + ¢ x (t) = t + 4 where: X (0) x² (0) = 0 X

A:

Q: Estimate 3x + x² using Mid-point method (n=6), then find the error estimate.

A: Given integral is ∫143x+x2dx. We have to estimate the given integral by using Mid-point method.…

Q: 4) Determine if the following statement is true and either prove it or provide a counter example:…

A:

Q: Exercise 4. For the function f(x) = x² + 2x² + 4x₁ + 4x2 prove by induction that the method of…

A: Solution : Given, f(x)=x12+2x22+4x1+4x2 ∇f(x)=2x1+44x2+4 ∇2f(x)=2004&gt;0 Applying method of…

Q: let f: R^ -> R be a function given by 2 f(x₁, x₂... x₁) x.x²2. x²n, where = € 2.1 Show that the…

A:

Q: “Assignment problem is a special case of transportation problem where the number of sources is equal…

A: To discuss: Assignment problem is a special case of transportation problem.

Q: Exercise 2. Obtain expressions for all first and second derivatives of the function of two variables…

A: Solution 2: Given function is f(x)=x14+x1x2+(1+x2)2           (1) Now, partially differentiating (1)…

Q: For the given probability density function, over the given interval, find the mean, the variance,…

A: This is a question from Theoretical Distribution.

Q: If M is an upper triangular matrix with integer entries then its eige Select one: O True

A: Introduction: A triangular matrix is a square matrix with all zeros below and/or above the diagonal.…

Q: Maximize z = 8x + 2y, subject to the following constraints. (If an answer does not exist, enter…

A: Given the equation: z=8x+2y constraints: 2x-5y≤10; -2x+y≤2; x≥0; y≥0   To find the maximum value of…

Q: 1. Consider the sequence defined by the explicit formula AN = N² +1. a) Find A₁ = b) Find A100 = c)…

A:

Q: 9.) Use spherical coordinates to evaluate 3/2 (x² + y² +2²) ³¹² dydzdx. 9-1² √√9-1²-₂² √√√9-x²-2²

A: To find the given integral using spherical co-ordinate system :-

Q: Wake Zsta is the square of an odd isteger, then the perfect squire of must be of the form

A:

Q: Write the Hindu Arabic numeral for the Roman numeral DLXIV

A:

Q: The value of B in the equation 3x+9y=1

A: Given: 3x+9y=1 To find: Value of b in given equation.

Q: 3. For each of the following normal curves, identify (as accurately as you can from the graph) the…

A: Follow the steps.