Let f (x) = x3. a. Find the second Taylor polynomial P2(x) about x0 = 0. b.

Question:

Let f (x) = x3.
a. Find the second Taylor polynomial P2(x) about x0 = 0.
b. Find R2 (0.5) and the actual error in using P2 (0.5) to approximate f (0.5).
c. Repeat part (a) using x0 = 1.
d. Repeat part (b) using the polynomial from part (c).

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Numerical Analysis

ISBN: 978-0538733519

9th edition

Authors: Richard L. Burden, J. Douglas Faires

See More Books

Question Posted: Mar 22, 2016 02:30 AM

See More Questions

Find the second Taylor polynomial P2(x) for the function f (x) = ex cos x about x0 = 0. a. Use P2 (0.5) to approximate f (0.5). Find an upper bound for error |f (0.5) P2(0.5)| using the error...
Find the third Taylor polynomial P3(x) for the function f (x) = (x 1) ln x about x0 = 1. a. Use P3(0.5) to approximate f (0.5). Find an upper bound for error |f (0.5) P3(0.5)| using the error...
Find the fourth Taylor polynomial P4(x) for the function f (x) = x(ex)2 about x0 = 0. a. Find an upper bound for |f (x) P4(x)|, for 0 x 0.4. b. Approximate c. Find an upper bound for the error in...
Nanette works for Piroz and is paid a basic wage of $1,000 a week. Piroz operates the following bonus scheme: (1) Each employee gets a bonus of $4 for every unit they produce in excess of 2,000 units...
As a loan officer for Allium National Bank, you have been responsible for the banks relationship with USF Corporation, a major producer of remote-control devices for activating television sets, DVDs,...
How is the experience and expression of emotion different in different types of jobs? Compare, for example, emotion in the work of a minister, a store clerk, and a data processor. Are the emotional...
Show that any two statistically independent random variables have a correlation coefficient that is zero.
The stockholders equity section of Jumes Corporations balance sheet consists of common stock ($8 par) $1,000,000 and retained earnings $300,000. A 10% stock dividend (12,500 shares) is declared when...
Under what circumstances do you think a company would seek private debt ( soliciting from a single party ) rather than public debt ( an open - to - the - public issuance, like a bond ) ?
Construct a payoff table for the various demand and stocking quantities. Determine the best amount to stock using regret (minimax). A market buys T-bone steaks from a universitys animal science...
Suppose f C[a, b] and f'(x) exists on (a, b). Show that if f'(x) 0 for all x in (a, b), then there can exist at most one number p in [a, b] with f (p) = 0.
Find the third Taylor polynomial P3(x) for the function f (x) = (x + 1) about x0 = 0. Approximate 0.5, 0.75, 1.25, and 1.5 using P3(x), and find the actual errors.
The volume expansivity b values of copper at 300 K and 500 K are 49.2 x 10-6 K-1 and 54.2 x 10-6 K-1, respectively, and b varies almost linearly in this temperature range. Determine the percent...
Suppose you have two identical-looking metal spheres of the same size and the same mass. One of them is solid; the other is hollow. Describe a simple test that you could do to determine which is...
A kangaroo carries her $0.51 \mathrm{~kg}$ baby in her pouch as she $\mathrm{BlO}$ bounds across the ground. As she pushes off the ground, she is accelerating upward at \(30 \mathrm{~m} /...
Riders on the Tower of Doom, an amusement park ride, experience $2.0 \mathrm{~s}$ of free fall, after which they are slowed to a stop in $0.50 \mathrm{~s}$. What is a $65 \mathrm{~kg}$ rider's...
A screwdriver with a very thick handle requires less force to operate than one with a very skinny handle. Explain why this is so.
An 80-ft-diameter Ferris wheel rotates once every $24 \mathrm{~s}$. What is the apparent weight of a $70 \mathrm{~kg}$ passenger at (a) the lowest point of the circle and (b) at the highest point?
You are told that a study is a 3 2 2 ANOVA. Make up variables and conditions and draw a diagram for the study.
The May 2014 revenue and cost information for Houston Outfitters, Inc. follow: Sales Revenue (at standard).............. $ 540,000 Cost of Goods Sold (at standard) ..........341,000 Direct Materials...
Use inerative refinement techniques to improve x 1 = 2, x 2 = 3, and x 3 = 8, which are approximate solution of 2x 1 + 5x 2 + x 3 = 5 6x 1 + 2x 2 + x 3 = 12 x 1 + 2x 2 + x 3 = 3
Consider vectors: A = 2i 3j + ak B = bi + j 4k C = 3i + cj + 2k Vector A is perpendicular to B as well as to C. It is also known that B.C = 2. Use any method studies in this chapter to solve for...
Consider the following vectors: A = ai + bj + ck B = 2i + j 4k C = I + 3j + 2k Where A is an unknown vector. If (A x B) + (A x C) = (5a + b)i + (3b - 2)cj + 9(-4c + 1)k Use any method learned in...
Sandy Bank, Incorporated, makes one model of wooden canoe. Partial information is given below. Required: 1. Complete the following table. 2. Suppose Sandy Bank sells its canoes for $510 each....
FIFO and LIFO costs under perpetual inventory system The following units of an item were available for sale during the year: 29 units at $44 Beginning inventory Sale 26 units at $64 First purchase 15...
Pie Corporation acquired 75 percent of Slice Company's ownership on January 1, 20X8, for $93,000. At that date, the fair value of the noncontrolling interest was $31,000. The book value of Slice's...

Let f (x) = x3. a. Find the second Taylor polynomial P2(x) about x0 = 0. b.

Question:

Step by Step Answer:

a P 2 x 0 b R 2 05 01...View the full answer

Numerical Analysis

Students also viewed these Numerical Analysis questions