Q.4: Find the third order Lagrange interpolation polynomial using the following table to compute f(9.2) from the following data; x f(x) 9 8 2.07944 2.19722 9.5 2.25129 11 2.39789

Q: (D-2)²y = 20 - 3xe²x

A:

Q: Questions: 1. What are the geometric means of the positive root? How about the negative root?

A: As per guidelines we are allowed to solve one question at a time so i am solving first one please…

Q: (a) Show that every compact subset of M is bounded. (b) Show that every contraction map f: M→M is…

A:

Q: Use the Midpoint Rule with n approximate the integral. 10 [." √x + 2dx = = 3 to

A:

Q: gallbladde it takes about 24 hours for the radiation levels to reach what we are exposed sity of…

A: Given the data as, t(hrs) 0 1 3 5 7 9 R 1.000 0.891 0.708 0.562 0.447 0.355

Q: Given that f(x)× ₂(x)= even function. If (x) is an odd function, therefore the correct f(x) is f(x)…

A: Given: The product of f1x and f2x is an even function. f1x is an odd function. To determine: The…

Q: 1 1 5 0 2 1 EEPEN -1 -2 0 3 -1 -1 7 2 -4 1 - -

A:

Q: Q.1B) Prove that: I = ₂ Cos(x) dxdy sin (1) 2 where R the region bounded by x + y = 1, x = 0, y = 0

A: Given that  I=∫∫RCosx-yx+ydxdy Where R the region bounded by x+y=1, x=0, y=0

Q: Find the sum of the series: n=0 1-2 (-1)" (1) " 2n + 1

A:

Q: B/ Put the following program in matrix standard form Min (z) = 10x₁+11x2 S.T. X₁+2x₂ ≤ 150 3x₁+4x₁…

A: Note: In the given question, the second constraint has to be of the form 3x1 + 4x2 ≤ 200 instead of…

Q: find the area of the surface S: x² + y² + 2² = 4 -A <tan -^ (*) FO 6 < COS Cos FJ VI (2) 4 DEX TI 3…

A: The given Surface is                    x2+y2+z2=4 ........1where π6≤tan-1yx≤π3 and π4≤cos-1z2≤3π4…

Q: 3. Calculate y at x = 1 and x = 2 in the following system; y"=10y' +5xy +10x +5 y (0)=10, y'(3)=20

A:

Q: $. 12-1 (2²+-)(2-2) 1-4z+6z² 1 -dz .d

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: อใน at2 4 อใน 0x2

A:

Q: Solve y" - 16 y = x ex

A:

Q: For the next three exercises, use series to evaluate the limit. (sinh)/h – cos h h² 1 lim 9-0 arctan…

A:

Q: = cosx (sinx). 2. Find the Fourier series on -≤x≤π for f(x) =

A: Given the function fx=cosxsin2x, -π≤x≤π

Q: Q3) for what values of (m) do the line (y = mx ) and the curve (y = 2+1) x²+1 enclosed a region ?…

A: given curves y=mx  and y=xx2+1 evaluate the intersection point mx=xx2+1⇒mxx2+1-x=0⇒xmx2+m-1=0⇒x=0 or…

Q: Question 2 If a function f is continuous at 0, show that g(x) = f(x) is differentiable at 0 and find…

A:

Q: Given the supply and demand functions of good p = x² + 2x + 12 p = -x² - 4x + 68 Calculate the…

A: The supply and demand functions of the product are respectively, p=xS2+2xS+12 and p=-xD2-4xD+68 To…

Q: 1. Determine all possible solutions of ²u ex² = d²u oy ² by using variable separable method. 7

A: The given problem is to solve the given partial differential equation by using the method of…

Q: . Find the critical numbers and then the critical points= of the functions. de 1₁ Y = - 3 Sketch the…

A:

Q: Which of the following graph represent the given periodic function? 2x+2, -2<x<0 0<x<2 44 0 --2 f(x)…

A: Explanation of the answer is as follows

Q: The Eigen value of matrix p is (solve) ГО 0 LO 1 0 0 1 -3 -4] (0,-1,-3) O (0,2,3) O (0,1,3) O…

A:

Q: 1. The following system has one root in the first quadrant. Perform one iteration to calculate the…

A: The Multivariate Newton Raphson method uses the formula: xn+1yn+1=xnyn-∂f1∂x∂f1∂y∂f2∂x∂f2∂y-1×fxnyn…

Q: Determine the form of a particular solution for the differential equation. Do not solve. y" + 14y'…

A:

Q: can you make introduction (explanation) about system of linear equation  and crout method the.…

A: Introduction to system of linear equation: System of linear equation occurs in variety of…

Q: Determine whether the following graph represents either even, odd or neither function: f(x) EVEN…

A:

Q: Problem 5. Are the following metric spaces compact? Prove your claims. (a) The integers Z with d(m,…

A:

Q: Consider the initial value problem: Solution: y' = (y -0.01x²)² sin(x²) + 0.02x; y(0) = 0.4 y =…

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer one question at a…

Q: Problem 2. To prepare for summer, Diffy E. Kew is trying out a new lemonade recipe. Through rigorous…

A:

Q: Solve the following Euler equation 2d²y +5 4x². + 5y = ln x

A: 4x2d2ydx2+5y=lnx let x=ez ⇒ z=lnx

Q: Given dy² c cos x + D sin x Cxe-* +4-5y = 2e*, the correct y, is (solve) Option 2 O Ce-x Cex Option…

A: given problem is  d2xdy2+4dydx-5y=2e-x clearly there is misprint in the first term it should be…

Q: 2. Using quadratic interpolation find In 9.2 from In 8.0=-2.0794, In 9.0-2.1972 and In9.5-2.2513.

A: The given problem is find the approximate value of ln(9.2) with given data points by using the…

Q: 23: Test convergence for th 1- En-o)(x + 5)"

A: According to the guideline I am answering only first question. 1- ∑n=0∞ 34nx+5n   Ratio Test : A…

Q: 1 - 27 S e+ix - x) w dw

A: As per the question we have to solve the integral from -∞ to ∞ And we will use Fourier transform and…

Q: 2. Let T: R³ R³ be the operator given by 1 1 T(v) = 9). 1 Determine whether T is decomposable or…

A: Consider the given operator, Tv=-1100-1100-1v Here we need to determine that whether T is…

Q: Q: - Find the centroid of the shaded area under the curve shown in the Figure below. 1. Use vertical…

A: The area under the curve y=f(x) and y=g(x)  where, f(x)&gt;g(x) using vertical stripe between the…

Q: 3. Determine whether the following integrals are convergent or divergent, and evaluate those that…

A: We know that , Improper integral of the function fx over interval -∞ , ∞ are of the forms ,  ∫a∞…

Q: The given analytic function f(z) = u + iv defines two families of level curves u(x, y) = c₁ and v(x,…

A: We know that a complex function is written as fz=ux, y+ιvx, y. Two families of curves are said to be…

Q: Determine the Cartesian Equation of a plane that has a normal vector (6,-5,12) and passes through…

A:

Q: Ex. Evaluate ff y ds where S is the portion of the cylinder x + y = 3 that lies between z= 0 and z=…

A:

Q: 1л 4 X Оп = 0 = 0.7853 Іл 2 Зл 4 п = 3.1416 = 1.5707 = 2.3561 f(x)= sen (2x) f(0п) = sen(2x0) = 0…

A: To Sketch: The graph of f(x)=sin(2x) for the given values in the table.

Q: Use the root test to find the radius of convergence for: xn nn n=1

A: Given series is ∑n=1∞xnnn   To Use: The root test in order to find radius of convergence of given…

Q: Q.2: Find the trigonometric Fourier series of the periodic function f(t), and show if it is odd or…

A: The given problem is to find the Fourier series expansion of the given periodic function with given…

Q: Question 1 Consider the points A(2,-1,0), B(3, 0, -2), and C(0, -3, -1). (a) Find the equation of…

A:

Q: Q3: Test convergence for the following series : 1- Eno)(x + 5)" n+1 2- 2n-one 3-

A: Note : As per our Guidelines we can solve first question. please repost remaining questions.

Q: If T: R³ R³ is a linear transformation such that then T = -3 12 -2 *(Q)-E}··(O)-E}··(O)-E] T = 3 T

A:

Q: Let F(x) = f(x5) and G(x) = (ƒ(x))5 . You also know that a¹ = 14, ƒ(a) = 3, ƒ'(a) = 8, ƒ' (a³) = 6…

A: Use the following formulae, to obtain the solution. Chain rule for differentiation:…

Q: The value f(x+y+z)dzdydx is (solve) 3/5 O 5/8 O 2/7 O 7/8 O

A: