For the given points Xo = 1, x =1.5, x, = 2.5 and x3 = 3. Find Lagrange Interpolation polynomial for the following function: f (x) = x² e* + In(sin x). %3D

Q: find the value of f(4) using the Lagrange's polynomial of at most degree3 from the data 3 5. y=f(x)…

A:

Q: Find the formula 1 [ f(x) dx = w₁f (0) + w₁f (1) that is exact for all functions of the form f(x) =…

A: Solution :-

Q: The function f(x) is approximated near æ = 0 by the second degree Taylor polynomial P2(x) = 5x – 5 –…

A:

Q: Find the denvatives of the following functions. 3at Зat i)x- 1+t' 1+t'

A: We have to find the derivative from the given parametric curve

Q: B/ Given a polynomial function with following data points: Find x f(x) 0 3.6 1.5 1.8 3 1.2 4.5 0.9 6…

A:

Q: The function f:R→R defined as fW)=log_lV\x²+1+x+VVx²+1-x) is

A:

Q: For the given points X, = 1, x =1.5, x, = 2.5 and x3 = 3. Find Lagrange Interpolation polynomial ww…

A:

Q: Given the following data which generated by the function y = 1/x. %3D X 1 2 4 5 y=f(x) 1 0.5 0.3333…

A:

Q: Find the antiderivatives following function. 1. f(x) =x' - 3x² +7x +e*

A:

Q: Find the nth Maclaurin polynomial for the function. f(x) = sin(x), n = 4 P4(x)

A:

Q: Find the nth Maclaurin polynomial for the function. f(x) = sin(x), n = 3 P3(x) =

A:

Q: 1. For the given functionsf(x), let xo= 0, x1=0.6 and x2=0.9. Construct interpolation polynomials of…

A:

Q: For the function f(x) = 21² + 1, it is given that 3 f(x) dx = 21. At what value C does the function…

A:

Q: Find the most general antiderivatives of the following functions. ƒ(x) = x² + 2x + 3

A: GIVEN: f(x) = x2 + 2x + 3

Q: For the function defined as follows, find the Taylor polynomials of degree 4 at 0.

A: The taylor series of the polynomial f(x)=ex at x=0 is defined as…

Q: 8. For the given function f(x) = v1+x, let ro = 0, x1 = 0.6, and r2 = 0.9. Construct an…

A:

Q: For the given points X, = 1, x, = 1.5, x, = 2.5 and x, = 3. Find Lagrange Interpolation polynomial…

A: We have to find out Polynomial using given values and function.

Q: Find the indefinite intergral of 1/(e^x -1)

A: To Find the indefinite intergral of 1/(e^x -1)

Q: Consider the following table: Xi 5 6 f(X) 7 12 14 Find f(4) using Lagrange method for interpolation.…

A:

Q: For the function f(x) = ln(x+1), let x0 = 1, ¤1 = 1.25, x2 = 1.6,the Lagrange interpolating…

A: Lagrange 2nd order  Interpolation formula:…

Q: Allow T2(x) be the 2nd degree Tylor polynomial for the following function: f(x)=2+x*e^(5x) which is…

A:

Q: Given that f(0) = 1, f(1) = 3, f(3) = 55, find the unique polynomial of degree 2 or less, which fits…

A: Solution is given:

Q: From a function, f(x), we obtain the following data points: (ri, f(x₂)) = {(-0.5, e³/2), (0, 1),…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the nth Maclaurin polynomial for the function. f(x) = sin(x), n = 6 P6(x) =

A: nth Maclaurin polynomial for the function :       Pn(x) =  ∑i=0n fi(0)i!xi = f(0)+f'(0)x + f''(0)…

Q: For the given points X, = 1, x =1.5, x, = 2.5 and x, = 3. Find Lagrange Interpolation polynomial for…

A: Given function is f(x)=x2esinx+ln(sinx) Find 'f(x)' corresponding to given values of 'x' x 1 1.5…

Q: 2. For the given functions f (x), let.x, = 1,x, = 1.25, and.x, = 1.6. Construct interpolation…

A: Step:- 1 Lagrange Interpolating polynomial:- P(x)=f0 L0(x) +f1 L1(x)+ f2 L3(x)+....fn Ln(x),Here,…

Q: Using the provided data, find the interpolated value of f(x) when x = 3 using Newton's Divided…

A:

Q: of Find and for the following function. f(x.y) = e 6xY In (5y)

A: The given function is: To find the partial derivative:

Q: 2. For the given functions f(x), let Xo 1,x 1.25, and.xy = 1.6. Construct interpolation polynomials…

A:

Q: In  the given equation as follows , find the nth Maclaurin polynomial for the function :- see the…

A:

Q: The cdf of checkout duration X for a book on a 2-hour reserve at a college library is given by: if…

A: We have given that the cdf, F(x) =  { 0,      if x<0              x2/4 ,  if 0<=x<2…

Q: 4. For the given function f(x) = /2 + x², let xo = 0, x1 = 0.5, and x2 = 0.8. Construct a Lagrange…

A:

Q: Find a general formula for f^n. f(x)=7x^2 e^x

A: Consider the given function fx=7x2ex. In order to find the nth derivative f'n, differentiate the…

Q: To approximate f'(xo), suppose first that ro e (a, b), where fe C (a, b), and that x1 = xo + h for…

A:

Q: Find the nth Maclaurin polynomial for the function. f(x) = eX, n= 5 Ps(x) = ||

A:

Q: Find the nth Maclaurin polynomial for the function. f(x) = sin(x), n = 6 Po(x) =

A: nth Maclaurin polynomial for the function f(x) :       Pn(x) = f(0)+f'(0)x +f''(0)…

Q: F(x) JO sin(7t) dt.

A:

Q: Fit a second order Newton's interpolating polynomial to estimate log 10 a) Interpolate using x, = 8,…

A:

Q: Approximate f(0.5) employing Lagrange interpolation polynomial with the nodes xo=0, x1=0.6, x2=0.9…

A:

Q: For the given functions f(x), let x, = 1,x1 = 1.25, and x, = 1.6. Construct interpolation…

A: PART A The given function is, f(x)=sin πx For x0=1 then f(x0)=0 For x1=1.25 then f(x1)=-0.7071 For…

Q: 3. For the following data set, find the interpolating polynomial by the Lagrange's Method. 2. 4.

A:

Q: if √0 =0, √T = 1 and √4 = 2 estimate √3 Compare by constructing Lagrange polynomial, ther with the…

A: Let  f(x)=x We have x f(x)=x 0 0 1 1 4 2 we have x0=0, x1=1, x2=4 Lagrange's polynomial…

Q: Find the nth Maclaurin polynomial for the function. f(x) = e*, n= 5 P3(x) :

A: Use maclaurin's series

Q: Approximate f' (1) using the given data f(0) = 1, f(1) = 2, f(2) = 1, and f(3) = 10 and the Lagrange…

A: Lagrange inteerpolation is used to find a polynomial equation which passes through the given set of…

Q: If R₂(x) is the second degree Lagrange interpolating polynomial for the data Xi Yi where the…

A:

Q: J(x) x cos (2x), To (a) Find Lagrange interpolating polynomial for f(x) using the three given nodes…

A: Given : fx=x cos2x -x2           x0 =0 ,  x1=0.3   x2=0.7 To Find :  Lagrange interpolation…

Q: Find the real root of the given function f(x) = e²x -x-6=0 by Newton-Raphson iterative method and…

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

Q: 1. For the given functions f (x), let xo = 0, x1 = 0.6, and x2 = 0.9. Construct interpolation…

A:

Q: Find the nth Maclaurin polynomial for the function. f(x) = sin(x), n = 5 P5(x) =

A:

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.