Homework Answers
Add Answer to:
3h Q6. Consider f'(X) f2 -f- hf"C) 2 1. Derive the formula using Taylor expansion. 2....
Section A Q1 0 Using the following Taylor series expansion: f(x+h) = f(x)+hf'(x)+22 h 3! f"(x)+...
Section A Q1 0 Using the following Taylor series expansion: f(x+h) = f(x)+hf'(x)+22 h 3! f"(x)+ (+0) (1.1) 4! show that the central finite difference formula for the first derivative can be written as: f'(x)= f(x+h)-f(x-1) + ch" +0(hº) (1.2) 2h Determine cp and of the derived equation. [4 marks] Consider the function: f(x) = sin +COS (1.3) 2 2 Let x =ih with n=0.25, give your answer in 3 decimals for (ii) to (vi): (ii) Evaluate f(x) for i...
(25 pts) For f(x) infinitely continuously differentiable, and C so that the formula Taylor series to...
(25 pts) For f(x) infinitely continuously differentiable, and C so that the formula Taylor series to find A,B, use Af (x 2h)Bf(x) Cf (xh) gives the highest order accurate approximation of f'(x) (for general f and x). What is that order? Remember, Taylor series says h2 |f" (x)^f"(x) h3 f(xh) f(x)hf'(x)+ ... 2! 3!
(25 pts) For f(x) infinitely continuously differentiable, and C so that the formula Taylor series to find A,B, use Af (x 2h)Bf(x) Cf (xh) gives the...
2. Use Taylor series expansions to arrive at the expression 1 3 1 f'(x) h f(x)2f(xh)...
2. Use Taylor series expansions to arrive at the expression 1 3 1 f'(x) h f(x)2f(xh) - f(x2h) 2 which we found in class using Lagrange polynomials
2. Use Taylor series expansions to arrive at the expression 1 3 1 f'(x) h f(x)2f(xh) - f(x2h) 2 which we found in class using Lagrange polynomials
(1 point) Consider the function f(x) = xin(x). Let T, be the degree Taylor approximation of...
(1 point) Consider the function f(x) = xin(x). Let T, be the degree Taylor approximation of f(2) about x = 1. Find: T = T = Use 3 decimal places in your answer, but make sure you carry all decimals when performing calculations T3 is an (over/under) estimate of f(2). If R3 is the remainder given by the Lagrange Remainder Formula: |R3|
2. Let 6 marks (a) Find f(x),f"(x), and f"(x). (b) Find the second order Taylor expansion of f at 1, namely f(r) = ao + ala-1 ) + a2(z-1)2 + R2(x), where Ra is the remainder. You s...
2. Let 6 marks (a) Find f(x),f"(x), and f"(x). (b) Find the second order Taylor expansion of f at 1, namely f(r) = ao + ala-1 ) + a2(z-1)2 + R2(x), where Ra is the remainder. You should find ao, a, a2, and R(p). 8 marks that the error in this estimation (i.e., R2(0.9)1) is at most 10-3. 6 marks (c) Use the Taylor expansion found above to estimate the value of f(0.9). Show Find f(x), f"(), and f" (b)...
Math Pratice Problems 1. Find the Taylor expansion of ex about c= 2. 2. Let f(x)...
Math
Pratice Problems 1. Find the Taylor expansion of ex about c= 2. 2. Let f(x) = ez?. Find f(10)(0).
5. Using Taylor series, derive the error term for the approximation f' (x) ~ -3 f(x) + 4 f(x + b)...
Please help me solve this. thanks
5. Using Taylor series, derive the error term for the approximation f' (x) ~ -3 f(x) + 4 f(x + b)-f(x + 2h)]. 2h
5. Using Taylor series, derive the error term for the approximation f' (x) ~ -3 f(x) + 4 f(x + b)-f(x + 2h)]. 2h
Q6. (20pts) Consider the function f(2)= cosh(z) (i) Let f(z) = Eno an izn be the...
Q6. (20pts) Consider the function f(2)= cosh(z) (i) Let f(z) = Eno an izn be the Taylor series expansion of f(z) around z = 0. Determine aj, aj, and a. (ii) Let f(z) = 2n-obn: (z - 14" be the Taylor series expansion of f(z) around z = 1 Determine bo, bı, and b2. Simplify the resulting expressions as much as possible.
Exercise 6: Given the table of the function f(x)-2" 2 X 0 3 2 f(x) 1 2 4 8 a) Write down the Newton polynomial...
Exercise 6: Given the table of the function f(x)-2" 2 X 0 3 2 f(x) 1 2 4 8 a) Write down the Newton polynomials P1(x), P2(x), Pa(x). b) Evaluate f(2.5) by using Pa(x). c) Obtain a bound for the errors E1(x), E2(x), Es(x) Exercise 7: Consider f(x)- In(x) use the following formula to answer the given questions '(x) +16-30f+16f,- 12h a) Derive the numerical differentiation formula using Taylor Series and find the truncation error b) Approximate f'(1.2) with h-0.05...
Question 3 (a) Grven that f(-2)= 46, f(-1) 4, J(1) 1, f(3)= 156, and f(4)= 484, formula to estimate f(0) Use four-d...
Question 3 (a) Grven that f(-2)= 46, f(-1) 4, J(1) 1, f(3)= 156, and f(4)= 484, formula to estimate f(0) Use four-decimal arithmetac with rounding use the Lagrange interpolation (8) (b) Why should the Lagrange formula be used in practice only with caution" (2) (e) Wnte down the system of equations that need to be solved in order Function for the following data to construct the natural cubic spline 30 -5 6790 -3 6674 3 1 32-22178 (8) Note You...
Section A Q1 0 Using the following Taylor series expansion: f(x+h) = f(x)+hf'(x)+22 h 3! f"(x)+ (+0) (1.1) 4! show that the central finite difference formula for the first derivative can be written as: f'(x)= f(x+h)-f(x-1) + ch" +0(hº) (1.2) 2h Determine cp and of the derived equation. [4 marks] Consider the function: f(x) = sin +COS (1.3) 2 2 Let x =ih with n=0.25, give your answer in 3 decimals for (ii) to (vi): (ii) Evaluate f(x) for i...
(25 pts) For f(x) infinitely continuously differentiable, and C so that the formula Taylor series to find A,B, use Af (x 2h)Bf(x) Cf (xh) gives the highest order accurate approximation of f'(x) (for general f and x). What is that order? Remember, Taylor series says h2 |f" (x)^f"(x) h3 f(xh) f(x)hf'(x)+ ... 2! 3!
(25 pts) For f(x) infinitely continuously differentiable, and C so that the formula Taylor series to find A,B, use Af (x 2h)Bf(x) Cf (xh) gives the...
2. Use Taylor series expansions to arrive at the expression 1 3 1 f'(x) h f(x)2f(xh) - f(x2h) 2 which we found in class using Lagrange polynomials
2. Use Taylor series expansions to arrive at the expression 1 3 1 f'(x) h f(x)2f(xh) - f(x2h) 2 which we found in class using Lagrange polynomials
(1 point) Consider the function f(x) = xin(x). Let T, be the degree Taylor approximation of f(2) about x = 1. Find: T = T = Use 3 decimal places in your answer, but make sure you carry all decimals when performing calculations T3 is an (over/under) estimate of f(2). If R3 is the remainder given by the Lagrange Remainder Formula: |R3|
2. Let 6 marks (a) Find f(x),f"(x), and f"(x). (b) Find the second order Taylor expansion of f at 1, namely f(r) = ao + ala-1 ) + a2(z-1)2 + R2(x), where Ra is the remainder. You should find ao, a, a2, and R(p). 8 marks that the error in this estimation (i.e., R2(0.9)1) is at most 10-3. 6 marks (c) Use the Taylor expansion found above to estimate the value of f(0.9). Show Find f(x), f"(), and f" (b)...
Math
Pratice Problems 1. Find the Taylor expansion of ex about c= 2. 2. Let f(x) = ez?. Find f(10)(0).
Please help me solve this. thanks
5. Using Taylor series, derive the error term for the approximation f' (x) ~ -3 f(x) + 4 f(x + b)-f(x + 2h)]. 2h
5. Using Taylor series, derive the error term for the approximation f' (x) ~ -3 f(x) + 4 f(x + b)-f(x + 2h)]. 2h
Q6. (20pts) Consider the function f(2)= cosh(z) (i) Let f(z) = Eno an izn be the Taylor series expansion of f(z) around z = 0. Determine aj, aj, and a. (ii) Let f(z) = 2n-obn: (z - 14" be the Taylor series expansion of f(z) around z = 1 Determine bo, bı, and b2. Simplify the resulting expressions as much as possible.
Exercise 6: Given the table of the function f(x)-2" 2 X 0 3 2 f(x) 1 2 4 8 a) Write down the Newton polynomials P1(x), P2(x), Pa(x). b) Evaluate f(2.5) by using Pa(x). c) Obtain a bound for the errors E1(x), E2(x), Es(x) Exercise 7: Consider f(x)- In(x) use the following formula to answer the given questions '(x) +16-30f+16f,- 12h a) Derive the numerical differentiation formula using Taylor Series and find the truncation error b) Approximate f'(1.2) with h-0.05...
Question 3 (a) Grven that f(-2)= 46, f(-1) 4, J(1) 1, f(3)= 156, and f(4)= 484, formula to estimate f(0) Use four-decimal arithmetac with rounding use the Lagrange interpolation (8) (b) Why should the Lagrange formula be used in practice only with caution" (2) (e) Wnte down the system of equations that need to be solved in order Function for the following data to construct the natural cubic spline 30 -5 6790 -3 6674 3 1 32-22178 (8) Note You...
Most questions answered within 3 hours.
-
Alternative
Classification
How to Estimate
Probabilities from Data? ( For continuous Attributes)
And How to generate...
asked 14 minutes ago -
Calculate the number density of argon gas at a temperature of
24C and a pressure of...
asked 12 minutes ago -
An explosion breaks a 20.0-kg object into three parts. The
object is initially moving at a...
asked 1 hour ago -
Calculate the approximate number of residues of Rubisco, which
is involved in carbon fixation in plants,...
asked 2 hours ago -
Other decisions about scientific claims can have a much broader
impact.ENERGYarrow-10x10.png, environment, health, security - all...
asked 3 hours ago -
I need to write a research paper and work cited about this
topic: The United States...
asked 3 hours ago -
Hello! I was wondering if I could have some help?
If the vapor pressure of carvone...
asked 3 hours ago -
An economist wants to estimate the mean per capita income (in
thousands of dollars) for a...
asked 4 hours ago -
What would be the input/output characteristic of a circuit
obtained by putting two of your 2's-complementers...
asked 4 hours ago -
In Drosophila, the transition from the syncytial blastoderm
stage to the cellular blastoderm stage is a...
asked 4 hours ago -
Project management question:
Name 3 different types of resources (hint: humans are one
type)
asked 4 hours ago -
Consider the following reaction: C 2H 2( g) + 2H 2( g) C 2H 6(
g)...
asked 4 hours ago