Choose the correct answerQuestion *Let f(x) = e* sin x.Using the forward 2-point formula for 1st derivatives with truncation error 1:f'(0) 0.3096 using h 1f(0) 0.5816 using h = 0.5Applying Richardson's extrapolation on the above values, we get a better approximationof f'(0) which is:0.85360.9897This optionThis optionNone of the answers0.9598This optionThis option

The derivative can be approximated using the Richardson approximation. The formula for the…

Let f(x) = e* sin x. Using the forward 2-point formula for 1st derivatives with truncation error 1: f'(0) 0.3096 using h= 1 f'(0) 0.5816 using h = 0.5 %3D Applying Richardson's extrapolation on the above values, we get a better approximation of f'(0) which is: 0.8536 0.9897

Let f(x) = e* sin x. Using the forward 2-point formula for 1st derivatives with truncation error 1: f'(0) 0.3096 using h= 1 f'(0) 0.5816 using h = 0.5 %3D Applying Richardson's extrapolation on the above values, we get a better approximation of f'(0) which is: 0.8536 0.9897

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Q: Using the forward difference and values of h=0.1, to approximate the derivative of cos(x) at…

A: This is a problem of Numerical Analysis.

Q: 1.x3 = at?, find the second derivative of "x" with ,d²x respect to "t", 'dt2

Q: evaluated at x = 0.001 and y = 0.002 Compute the derivative of the following: 5 g(x) =, 2.1'x f(x) =…

A: topic - derivative of a function

Q: The function f(r) = tanh(r) is one-to-one and so is invertible. Using our rule/ formula for relating…

A: Given that

Q: 4) fG) = (2x+ 1)9 %3D

Q: 4. Find the first derivative of the given function using the Rules of Differentiation: a. h(x) = X-…

Q: Q4. First approximate the derivative of the following function at xo = 1 using three-point midpoint…

A: Given fx=excos x, h=0.25 We can solve this by using formula and given information

Q: Let f(x) = ln x. By using the following formula for first derivative approximation: - - f'(x) ≈ f (x…

Q: Estimate the true percent relative error for the first derivative of the function, y = cos(sin(x)+…

A: We have to find 1st derivative using central difference method and then calculate true percent…

Q: A-The derivative is y = ln sin 0 cos 0 1+2ln 0

Q: find the derivative of y with respect to the appropriatevariable. y = s√(1 - s2) + cos-1 s

Q: Use forward-difference formula to evaluate the first derivative of y = cot(x) at z =; using a value…

A: Given, y=cotx at x=π2 , h=π4

Q: dy of the function dæ Find the derivative x* In 3y = y sin 3x + et.

Q: Q3: Find the first derivative of y= cos(x) at x= t/2 using a step size of h= Tt/12. Use forward and…

Q: Compute the high-accuracy central difference approximation for the first derivative of y = cos x at…

A: There are three types of approximations to the derivative of a function f(x) at a point a. They are…

Q: Find the differential equaiton corresponding th y= a cos(log x) +b sin(log x) where a and b are…

A: Differential equation formation

Q: Find the derivative of the following function. y = In (x° +6)" dy %3D dx (Type an exact answer,…

A: Given: y=ln(x3+6)π To find the dydx=?

Q: ) Using the Richardson’s extrapolation, to calculate a more accurate approximation for the second…

Q: Use forward and backward difference approximations of O(h) and a centered difference approximation…

A: Step:-1 Note:- 1. Forward difference approximation for first derivative f'x ≈fx+h-fxh 2. Backward…

Q: Q1. (a) Show that the following function is continuous at x = 1 for all values of p. spx + 1, if x >…

Q: . Compute the central difference approximations of O (h^4) for the first derivative of y = cos(x) +…

Q: Find the derivative of y with respect to 0. y = In (4 cos20) dy de

A: Given, y = ln4cos2θ We have to find dydθ

Q: Use forward-difference formula to evaluate the first derivative of y = tan(r) at a = using a value…

A: We know that the forward difference formula is: f'(x)=f(x+h)-f(x)hThe given function is : y=tan(x)We…

Q: find the derivative of y with respect to x, t, or θ, as appropriate.

Q: • Find f (x) of f(x)= by using the definition of the x-1 derivative. • 1- Find if y=3t-4 and t Vx+…

A: we have to find the derivative using definition. as per definition f'(x)=limh→0f(x+h)-f(x)h

Q: Find the derivative of y with respect to x, and 0 as appropriate: y = 6(sin (In 6) + cos (In 6) а.)

A: Given equation is: y=θsinlnθ+coslnθ Differentiate each term of y with respect to θ:…

Q: Given the function below: Approximate the following using h = 0.2: f(x) = ex cos(x²) a. First…

Q: Find the (a) approximate error and (b) relative approximate error of the following: The derivative…

A: Note:- For this problem, you don't mention any particular method and anything about h. So, I'll try…

Q: 6. y = In (e* + e") 7. y = tan e + etanax 8. y = In(x + Vř +1) 9 y = Arctan(;

Q: Estimate the true percent relative error for the first derivative of the function, y = e*cos(x?), at…

Q: Let y = In(x'e2x ). Find dy/dx.

Q: Find the derivative y = e* In x In x ex E + e* In x O None of these

A: Use product rule:-

Q: Use forward-difference formula to evaluate the first derivative of y = cos(x) at x = using a value…

A: Given we have given the function y=cos(x) we have to find the first derivative of y = cos(x) at x =…

Q: The average rate of change of f(x) = cos(x) with respect to x as a changes from 0 to π is 2 OOO 2 -2…

A: We have to find the average rate of change.

Q: Let f (x) = 2 Using the centered 3-point formula for 1st derivatives: %3D (x+1)3" www f'(0) ×…

A: Solution:

Q: Evaluate the derivative of e22.1.png acos(b/x) COS f(x) = x2 if a = 71 and b = 0.5 at x = 2 using…

Q: 29. Prove the following derivatives by using the definition of derivative. (a) (") = n. dx nxn-1

A: topic - derivative and limits

Q: Let ((x) = e" sin x. Using the forward 3-point formula for 1st derivatives with truncation error 2:…

A: The Richardson extrapolation can be used to calculate the derivative of the function at a point. The…

Q: If y = cos x, then the nth derivative of y with respect to x is equal to itself if n is a natural…

A: 9. y =cosx nth derivative and n is divisble by 4 it means n is even number 4,8,12...ny so lets…

Q: 10. Let y = In(x' + sin 3x). Find dy/dx.

Q: Solve for the derivative of the given implicit functions. a. Find dy/dx for y= ln (4x+tan-1(lnx)).…

A: Solve: a. Find dy/dx for y= ln (4x+tan-1(lnx)). b. Find dy/dx for y= tan-1 (3x-2 sinx). c. Find the…

Q: Find the derivative of the following function. y= In (x +8)* dy dx (Type an exact answer, using x as…

Q: Use a forward difference to approximate the derivative of f (x) at x = using h = 0.0001 -0.86627526…

Q: 4. Find the second-order derivative of the following function: f(z) = log, cos z + In %3D

Q: Show that the following function is continuous at x = 1 for all values of p. (px + 1, if x > 1 f (x)…

Q: Find the actual error when the first derivative of f(x) = sin(2x) at *=1/8 s approximated by the…

Q: Find the derivative of y with respect to x: ,2 2 X'e y = log,2 x+2) Evaluate the integral: -1 cos…

Q: Using the three-point midpoint formula, find the approximate value of the fist derivative of f(x) =…

A: To approximate the value of the first derivative of the below function at x=2 with h=0.1. fx=xex

Q: Define h(x) = x° sin(1/x) for x # 0 and h(0) = 0. Prove that h is differentiable at x = 0, and find…

Q: QS:-Find the first order derivative of each of the following functions: a) y = etan"x + In (sin-x)…

Question

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Numerical Differentiation$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

Use central-difference method to approximate the derivative of f(x) = In x² with value of x at 1.8, using a step size of 0.5. Satisfy the 0.05% acceptance criteria.
Use Richardson extrapolation to estimate the first derivative of y = cos x at x = π/ 4 using step sizesof h1 = π/ 3 and h2 = π/ 6. Employ centered differences of O(h2) for the initial estimates.
Use Richardson extrapolation to find an improved estimate for the first derivative of y = cos x at x =π/4 using step sizes of h1 = π/3 and h2 = π/6. Employ centered differences of O(h2) for the initial estimates. Discuss from your results the effect of using Richardson extrapolation on the error of using centered differences.
Obtain the first derivative of the function f (x) = sinx/x using Richardson's extrapolation with h = 0.2 at point x= 0.6, in addition to obtaining the first derivative with the 5-point formula, as well as the second derivative with the formula of your choice .
Apply central divided difference approximation (CDD) to find the first 5 derivative of F(x) = e0.8x at x = 24 using a step size of 1.3.
At the x value which is closest to 44, calculate the derivative of f(x) using a suitable second order accurate finite difference method with a) h = 25, b) a different step size. (You should use the same finite difference method in (a) and (b)). Using the values you calculated at parts (a) and (b) apply Richardsonextrapolation to improve your calculation.
find the first derivative and solve it for x after setting it to zero. Substitute the x-values obtained as well as your endpoints into the original functions to observe the y-values. Only subs x-values that lie within the closed interval given.
8) Find the first derivative or f’(x) of the following functions using the techniques of integration:
Compute the required derivative approximations for the functions at the specified location, for the specified step size, and specified method. 2. SECOND DERIVATIVE: Three-point forward y = (x^2) cos x ; at x = 0.4, h = 0.1
Please kindly use chain rule on the below to find the derivative and label all parts. h(x)= cos (x4) Identify all the parts in the below chain rule using this below formula h(x)=f(g(x)) h'(x)=f'(g(x))g'(x)
Find the Differential Eq (particular and general)
2)Find the first derivative or f’(x) of the following functions using the techniques of integration: