2. Use central-difference method to approximate the derivative of f(x) = ln x² with valueof x at 1.8, using a step size of 0.5. Satisfy the 0.05% acceptance criteria. 3. Approximate the integral of f(x) = x² − 2x + 4 with the following unequally spacedpoints shown in the table using Trapezoidal rule. What is the absolute relative error?Xo0X10.1X20.3X30.6X41.04. Find f'(5) using backward difference method of the function7x³5x + 1f(x)2x¹ + x² + 1with a given step size of h = 0.5. Satisfy 0.1% acceptance criteria.5. Given the functionf(x) = 1 + e* sin(4x)with integration limits from a = 0 to b= 1. Use Trapezoidal Rule and Simpson's 1/3 ruleto calculate the approximate value with n = 6. Get the relative error of both methods.=

As multiple questions are there and it is not mentioned that which question to be solved, I will…

Answered: central-difference method to…

central-difference method to approximate the derivative of f(x) = ln x² with value Use of x at 1.8, using a step size of 0.5. Satisfy the 0.05% acceptance criteria.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter4: Calculating The Derivative

Section4.2: Derivatives Of Products And Quotients

Problem 36E

See similar textbooks

Related questions

Q: dy-x+y+2 10. Solve the differential equation = if the solution curve passes dx - x + y + 3 through…

Q: The second-order Adams-Bashforth method for the integration of a single first-order differential…

A: Problem is solved using concept of second-order Adams-Bashsorth Method.

Q: 9. For the differential equation condition y(0) = 1. dy -- y = ey², solve for y = f(x) given the…

Q: 4. Use the Divergence Theorem to evaluate the flux integral JS, F-ndA over the surface of a…

A: Given that, F=(3xy3z5,3y,-xy3z6)F⇀=3xy3z5i^+3yj^-xy3z6k^ We have to evaluate the integral ∫∫sF⇀.ndA…

Q: all parts if quesion thanks

A: a. (i) Given, ∫14x2+9dx

Q: 13. U(5) Z4 True ● False 14. A subgroup of a group is a left coset of itself. True False ●

Q: Use the calculus of residues to evaluate the improper integral COSX -dx. (x²+1)³

Q: f(s) = s²+5 3s3+2s2+5s find f(t)

Q: find solution using direct integral method for the partial differential equation below: 2³7 1 = 12…

A: Here we using integration w.r.t to x and y to find this

Q: y" - 2y' + y = 4e-t + 2et, where y(0) = -1, y'(0) = 2

Q: Using the previous tax table, compute the tax liability for the individual in the scenario…

Q: 10. The set of automorphisms of a group is a group under the operation of function composition. True…

A: Isomorphism : A bijective mapping that preserves binary compositions in both groups is called…

Q: The two directed graphs below are isomorphic. Select one: True False

Q: Q1.a) Leta (4563 • vany vigill b) Let T be a cofinite topology on a set of real numbers R and A =…

A: This is a question of Topology.

Q: what is the equation of fo

A: Given, Vi Pi 2.27 2500 2.4 1000 3.31 5491 3.27 23700 3.85 78200 3.7 14000 4.81…

Q: Your parents helped you buy a car. You were supposed to pay then back $2000 sixty days ago and $1800…

A: Solution:-

Q: 3.1 Let S be the set of all bounded continuous functions f: [a, b] → R. Given two points f and g in…

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

Q: In the use of RSA Cryptography, for the public key (11, 65), what is the decrypted original message…

A: Solution :-

Q: In a manufacturing process, the diameter of steel rods is distributed normally with a mean value of…

Q: In formal symbolic logic, show that [P&∼P]⊃Q is a theorem.

A: This is a problem of Logic.

Q: Denote the Euler-method solution of the initial- value problem dx 1 dt xt = x(1) = 1 using step size…

A: Pseudocode Algorith Pascal Program

Q: Let f: N N be the function defined by f(n) = n(n) for all n E N, where is the Euler Phi Function.…

Q: Use a graphing calculator to calculate B, B², B³,... and AB, AB², AB³,... Describe any patterns you…

A: Let us calculate manually how to find B^2 using matrix multiplication. We will calculate B^2 using…

Q: 12. Given the differential equation x dx = 0 and one solution y₁ = A (constant), use reduction of…

Q: 5. In how many ways can 7 boys be seated in a circular order?

Q: 3. Find the Maclaurin series of the function F(x) = foedt. Use it to estimate F(1/2) with an error…

A: We will use Maclaurin series of ex ex=1+x1!+x22!+x33!+......∞

Q: A) Consider the vector-field F(x, y) = 2xy³i+ 3y²x²j. 1. Show that F is conservative. 2. Find a…

Q: give follow (a) the volume of R using cylindrical coordinates with dV = r dz dr de where R: 0≤ x≤…

A: set up the integral (a) the volume of R using cylinderical coordinates with dV=r dz dr dθ where…

Q: Find the Taylor series for f centered at 5 if f(n) (5) (-1)^n! 3^(n + 2) Σ (1 ]) n = 0 What is the…

Q: If the simple graph G has v vertices and e edges, how many edges does the complement of G have? Ⓒa.…

Q: Consider the curve formed by the parametric equations below. Which of the following statements DOES…

A: Follow the steps.

Q: Set up the triple integral that will give the following: (b) the volume of the solid B that lies…

Q: A periodic function is defined by -π, -π<t < 0, f(t) = {; nt, 0 ≤ t < π, f(t + 2π) = f(t). This…

Q: and if the rectum AB=AC втс Sos LABSBC and BCLAB ABE B CundBC сав 2 завж вс 4AB- Вс 5 All of the…

A: Here we take a example then solve this problem.

Q: Given F(x, y) = x² + y² and the system of ODEs 3 x = y, y = -x + Y what is the value of along…

Q: 2.3.9 Using the third-order Adams-Bashforth method (start the process with two second-order…

A: Write the Adams-Bashforth Predictor formula as follows:

Q: You recently bought a Shark robot vacuum. The rectangular region of your family room has the…

Q: 6-Assuming that the following fixed-point iteration converges 3 www. + 1/ (+ + ²/2 ) Xk+1 a-√3 c- √5…

Q: y" - 2y' + y = 4e-t + 2et, where y(0) = -1, y'(0) = 2

Q: f(s) = s² +5 2 3s³+2s²+5s find f(t)

Q: 2 if A= /3 12 If 057 9 1-4, B- 30 -1 4-62 that i) A+B = 1/2 (2A + 2B :') (AB)" =B³A² ii) -1 "A")…

A: Addition of matrix is defined if the matrices are of same order and is obtained by adding…

Q: Q #2. Explain how the graph of g is obtained from the graph of f. Graph both f and g on the same…

A: The vertical shift in the graph of y=f(x) is represented by the transformation function: y=f(x)±n.…

Q: 2. Let N (x) be the statement "x has visited North Dakot where the domain consists of the students…

A: There exists a student who has visited North Dakota

Q: (a) Set up the Newton's method to solve the following nonlinear system of equations ((,0)=0 Then…

A: given, f(x,y)=3yx2-10x+7=0g(x,y)=y2-5y+4=0let's say f(x,y)=f1 and g(x,y)= f2

Q: Determine y(t) Lly ✓ 3. y" 13y' + 40y = 0, where y(0) = 0, y'(0) = -2 -

Q: C is the intersection curve between the paraboloid z=x²+y² and

A: Given that C is the intersection curve between the paraboloid z=x2+y2 and the cylinder x2+y2=1.

Q: 2. Use Euler's method to solve the O.D.E ý = y² + ex for 0≤x≤ 1, step = 0.1 with initial condition…

Q: (c) (i) Find all the square roots of 1 in Z25 and Z32. Find all the square roots of 9 in Z800- (ii)…

Q: Set up the triple integral that will give the following: (a) the volume of R using cylindrical…

A: —

Q: A periodic function is defined by f(t)= ={₁ -, πt, -<t<0, 0 ≤t<π, f(t + 2π) = f(t). This function is…

Question

2. Use central-difference method to approximate the derivative of f(x) = ln x² with value
of x at 1.8, using a step size of 0.5. Satisfy the 0.05% acceptance criteria.

3. Approximate the integral of f(x) = x² − 2x + 4 with the following unequally spaced
points shown in the table using Trapezoidal rule. What is the absolute relative error?
Xo
0
X1
0.1
X2
0.3
X3
0.6
X4
1.0
4. Find f'(5) using backward difference method of the function
7x³5x + 1
f(x)
2x¹ + x² + 1
with a given step size of h = 0.5. Satisfy 0.1% acceptance criteria.
5. Given the function
f(x) = 1 + e* sin(4x)
with integration limits from a = 0 to b= 1. Use Trapezoidal Rule and Simpson's 1/3 rule
to calculate the approximate value with n = 6. Get the relative error of both methods.
=

Expert Solution

This question has been solved!

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

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

using 3 points Central difference formula

VIEW

Using 5 point Central difference formula

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here