Homework Answers
Approximating derivatives f(z +h) - f(z) f(x)-f( -h) f(x + h) - f(x - h) Forward difference Backw...
Added the formulas, thank you!
Approximating derivatives f(z +h) - f(z) f(x)-f( -h) f(x + h) - f(x - h) Forward difference Backward difference Centered difference for 1st derivative s(a) (3) 2h t)-2e-bCentered diference for 2nd derivative (4) 2 2. Write a short program that uses formulas (1), (3) and (4) to approximate f(1) and f"(1) for f(x)e with h 1, 2-1, 2-2,.., 2-60. Format your output in columns as follows: h (6+f)() error (öf(1 error f error Indicate the...
4. For f(x) = e-* and h = 0.10 where, C = 1.** a) Use centered...
4. For f(x) = e-* and h = 0.10 where, C = 1.** a) Use centered approximations to estimate the first and second derivatives of f(x) at x = 2. Use the east accurate formulas available. (10 pts) b) Using the most acurate forward and backward difference formulas, estimate the first derivative of f(x) at x 2. (10 pts) Forward Difference First Derivative 7.) - SD Error OM or) = -1.) + 40..) - 3 ) 2h Second Derivative 'w...
Differentiate the following function: f(x) = ex -2x +1
MatlabMECE 2350 Numerical Methods Lab 8.1. Differentiate the following function: f(x) = ex -2x +1 and solve its first derivative atx = 8 2. Numerically evaluate the approximated first derivative from the above function at x = 8 and h = 0.15 by the following: (a) Forward finite difference method (b) Backward finite difference method (c) Centered finite difference method 3. Calculate the error of each method by comparing the numerical derivative with the result from problem 1.
(a) Use the following data to find the velocity and acceleration at t = 10 seconds:
Numerical methods(a) Use the following data to find the velocity and acceleration at t = 10 seconds:Time (s):0246810121416Position (m):00.71.83.45.16.37.38.08.4Use second-order correct (i) centered finite-difference, and (ii) backward finite-difference methods. (b) Use the Taylor expansions for f(x +h), f(x+2h), f(x +3h) and derive the following forward finite-difference formulas for the second derivative. Write down the error term$$ f^{\prime \prime}(x) \approx \frac{-f(x+3 h)+4 f(x+2 h)-5 f(x+h)+2 f(x)}{h^{2}} $$
Numerical Analysis hr2 h 2 f(x) = a. x3. e-(0.1)x -- +4. x. In(x) – 1500...
Numerical Analysis
hr2 h 2 f(x) = a. x3. e-(0.1)x -- +4. x. In(x) – 1500 = 0 VX + 2 We want to find the root of the above equation. (In order to ease the reading, points are used between variables. Only the number above “e” is equal to “zero point one”.) b) If "a=1.5” and “b=0.8" at the above function, find the root between Xa=50 and Xu=70 using method of false position “Regula-Falsi” until Ea of approximation satisfies...
Part II (Numerical Analysis, 50pt) Consider the following differential equations with x and y as outputs,...
Part II (Numerical Analysis, 50pt) Consider the following differential equations with x and y as outputs, and iu as a unit step input ? 0.5y + ??, Develop the iterative equation based on the forward difference method for this system in terms of dt
3. For f(x) = e-x and h = 0.6
3. For f(x) = e-x and h = 0.6 a) Use forward and backward difference approximations to estimate the second derivatives of f(x) at x = 2. Use the least accurate formulas available.b) Using the most accurate centered difference formula, estimate the second derivative of f(x) at x=2.
2. Show that the approximation 2 1 h) - 5(x- h)- S(x + 2h) - f(x- 2h) (x) can be obtained by a Richardson extrapola...
2. Show that the approximation 2 1 h) - 5(x- h)- S(x + 2h) - f(x- 2h) (x) can be obtained by a Richardson extrapolation. [Hint: Consider (h) f(z+2h)-f(x-2h) 2h
2. Show that the approximation 2 1 h) - 5(x- h)- S(x + 2h) - f(x- 2h) (x) can be obtained by a Richardson extrapolation. [Hint: Consider (h) f(z+2h)-f(x-2h) 2h
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
2. (25 pts) Numerical differentiation. Numerical implementation. a. Compute the forward, central, and backward numerical first...
2. (25 pts) Numerical differentiation. Numerical implementation. a. Compute the forward, central, and backward numerical first derivative using, 2, 3, and 4 points for the function y = cos x at x = 7/4 using step size h = /12. Provide the results in the hard copy. Note that the central differences can only be apply for odd number of points ). b. Provide the analytic form of the derivatives, as well as table of the computed relative error for...
Added the formulas, thank you!
Approximating derivatives f(z +h) - f(z) f(x)-f( -h) f(x + h) - f(x - h) Forward difference Backward difference Centered difference for 1st derivative s(a) (3) 2h t)-2e-bCentered diference for 2nd derivative (4) 2 2. Write a short program that uses formulas (1), (3) and (4) to approximate f(1) and f"(1) for f(x)e with h 1, 2-1, 2-2,.., 2-60. Format your output in columns as follows: h (6+f)() error (öf(1 error f error Indicate the...
4. For f(x) = e-* and h = 0.10 where, C = 1.** a) Use centered approximations to estimate the first and second derivatives of f(x) at x = 2. Use the east accurate formulas available. (10 pts) b) Using the most acurate forward and backward difference formulas, estimate the first derivative of f(x) at x 2. (10 pts) Forward Difference First Derivative 7.) - SD Error OM or) = -1.) + 40..) - 3 ) 2h Second Derivative 'w...
Numerical Analysis
hr2 h 2 f(x) = a. x3. e-(0.1)x -- +4. x. In(x) – 1500 = 0 VX + 2 We want to find the root of the above equation. (In order to ease the reading, points are used between variables. Only the number above “e” is equal to “zero point one”.) b) If "a=1.5” and “b=0.8" at the above function, find the root between Xa=50 and Xu=70 using method of false position “Regula-Falsi” until Ea of approximation satisfies...
Part II (Numerical Analysis, 50pt) Consider the following differential equations with x and y as outputs, and iu as a unit step input ? 0.5y + ??, Develop the iterative equation based on the forward difference method for this system in terms of dt
3. For f(x) = e-x and h = 0.6 a) Use forward and backward difference approximations to estimate the second derivatives of f(x) at x = 2. Use the least accurate formulas available.b) Using the most accurate centered difference formula, estimate the second derivative of f(x) at x=2.
2. Show that the approximation 2 1 h) - 5(x- h)- S(x + 2h) - f(x- 2h) (x) can be obtained by a Richardson extrapolation. [Hint: Consider (h) f(z+2h)-f(x-2h) 2h
2. Show that the approximation 2 1 h) - 5(x- h)- S(x + 2h) - f(x- 2h) (x) can be obtained by a Richardson extrapolation. [Hint: Consider (h) f(z+2h)-f(x-2h) 2h
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
2. (25 pts) Numerical differentiation. Numerical implementation. a. Compute the forward, central, and backward numerical first derivative using, 2, 3, and 4 points for the function y = cos x at x = 7/4 using step size h = /12. Provide the results in the hard copy. Note that the central differences can only be apply for odd number of points ). b. Provide the analytic form of the derivatives, as well as table of the computed relative error for...
Most questions answered within 3 hours.
-
what statement accurately depicts the similarities in
requirements between payroll and human resources function
asked 1 hour ago -
Calculate the volume integral of the function T=z^2 over the
tetrahedron with corners (0,0,0), (1,0,0), (0,1,0),...
asked 3 hours ago -
I propose to you a game. You roll 2 dice. If the sum of the
numbers...
asked 3 hours ago -
Select the most likely lattice types for each of the following
salts: (a) BeF2; (b) CaO;...
asked 4 hours ago -
a
ball is thrown downward with velocity of 10m/s. calculate the final
velocity if it reaches...
asked 4 hours ago -
How many grams of ice at -15°C must be added to 705 grams of
water that...
asked 6 hours ago -
2. Balance sheet
The balance sheet provides a snapshot of the financial condition
of a company....
asked 6 hours ago -
In week 1 of the chemical equilibrium experiment, you and your
lab team will create a...
asked 7 hours ago -
Identify and describe five (5) characteristics of a good KM
measurement system. Be sure to include...
asked 7 hours ago -
What are at least five (5) workplace wellness best practices for
a successful wellness program? Explain...
asked 6 hours ago -
A pharmaceutical company is testing a new drug. Of the 110
people that received the drug,...
asked 7 hours ago -
Which of the following is NOT a mechanism for gene
regulation?
a. Phase variation in DNA....
asked 7 hours ago