(This is closely related to "Taylor polynomials" which appear at the end of 1st year calculus.)

Q: R E Given: m BE = 36 тве Y L LEYL is a right angle M LEYR = 77

A:

Q: 6 (iv) (v) (8) 5

A:

Q: Prove Taylor's theorem.

A: The objective is to prove Taylor's theorem. According to Taylor's theorem we have, If fx be a…

Q: What are Taylor polynomials? Of what use are they?

A: Let us take a function f, a specific point x = a (called the center), and a positive integer n, the…

Q: Q2) Find the expansion in Legendre polynomials of the functions: a) f(x)=2-x-x² x) = { 1 ) 0, b)…

A: We have to find the expansion in Legendre polynomials of the function.

Q: (22) Let A = (-∞, -2] and B = (102, ∞).

A: Given A=(-∞, -2] , B=(102, ∞). Now, the union of two sets consists all those elements that belong to…

Q: 4. An interpolating polynomial of degree 20 is to be used to approximate e-² on the interval [0,2].…

A:

Q: When using yi=f(xi) for i=0,1, ..., n to find the Lagrange interpolating polynomial ---p(x), p(xi)…

A:

Q: Find the Taylor the function at point a f(x) = In x, a=1

A:

Q: What is the nth Taylor polynomial of a function f(x) at x=c?

A:

Q: Use the function f(x) = 5x – 6 to compute and expand and simplify the following. a. f(-) = b. f(-6a)…

A:

Q: Consider the Lagrange polynomial that passes through the 4 data points given by 2 8 y 7 | 151 | 407…

A: We know that L0x is given by  L0x=x-x1x-x2x-x3x0-x1x0-x2x0-x3        1 Here, x0=2,x1=5,x2=7,x3=8,x=4…

Q: 5x+h over 5x+h+3 minus 5x over 5x+3, all over h. This is a difference quotient problem in…

A: LCD of the numerator is (5x+5h+3)(5x+3).We make both denominators same then subtract the rational…

Q: Determine the recursive definition for the function f(n) = n + 2", where n ≥ 0.

A: Determine the recursive definition for the function f(n) = n + 2 , where n≥ 0.

Q: The polynomial that passes through the following (x, f(x)) data 18 22 24 f(x) ? 50 246 is given by…

A:

Q: (2) Construct the Simpson 3/8-th formula to approximate f(x)dr by using La- grange interpolating…

A: Given: ∫abf(x) dx and the function f(x), where the interval of integration a, b is divided into n=3…

Q: Consider the recursive definition of the function f(n) f(0) = 0 f(n) = 1+ f(n-1) Find ƒ(1), ƒ(2),…

A: Recursive relation: It is an equation which represent a sequence based on some formula. From the…

Q: Find the index of 5 relative to each of the primitive roots of 13 (a) 2 (b) 6 (c) 7 (d) 11

A: To find the index of 5 relative to each of the primitive roots of 13. We know that p be prime number…

Q: Suppose f(x) = f* (e True or false: The function f is strictly increasing. True False (612 - 1) dt…

A:

Q: Suppose L(x) = "x is a llama" and E(x) = "x is an emperor." Do the following to statements mean the…

A: Consider the given information:

Q: Compute the following values, showing your work: φ(20), φ(25), φ(54) and φ(8!)

A:

Q: Find the polynomial f(x) for which x· f(x – 1) = (x – 3) · f(x), Væ |

A: find the polynomial f(x) for which  x fx-1=x-3 fx ∀x for x=0 x fx-1=x-3 fx ∀x

Q: Write the recursive definitions suitable for the following functions in the fields in the table. f…

A: We have to write recursive definitions suitable for the following functions in the fields in the…

Q: Ž ( – 1)"x" 1+x

A: Given the power series

Q: 1. Legendre functions for n = 0. Show that (6) with n = 0 gives Po(x) = 1 and (7) gives (use In (1 +…

A: The given differential equation is (1-x2)y"-2xy'+n(n+1)y=0 and…

Q: xy

A: (1/4)(x²y² - 2) - (xy + 1/2)² = (1/4)(x²y² - 2) - (x²y² + xy + 1/4) = (-3/4)x²y² - xy - (3/4) Or you…