Suppose that (f) is a quadratic polynomial. Prove that for (delta in mathbb{R}), [f(x+delta)=f(x)+delta f^{prime}(x)+frac{1}{2} delta^{2} f^{prime

Question:

Suppose that $f$ is a quadratic polynomial. Prove that for $\delta \in \mathbb{R}$,

\[f(x+\delta)=f(x)+\delta f^{\prime}(x)+\frac{1}{2} \delta^{2} f^{\prime \prime}(x) .\]

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

Step by Step Answer:

Related Book For book-img-for-question

Introduction To Statistical Limit Theory

ISBN: 9780367383138

1st Edition

Authors: Alan M. Polansky

See More Books

Question Posted: Mar 15, 2024 02:01 AM

See More Questions

Graph the functions g(x) = 1 - X, 2 - X, 0 x 1 1 < x < 2
In Exercises 1 through 28, differentiate the given function. 1 8 f(x) = 11/16 4 2 - x + 2
Evaluate the integral. .2 + 2 dx x + 2
Assume that the marginal product of capital is given by the following expression: MPK = 60/K^0.7 (K is measured in trillions). a) Graph the demand curve for capital and find the equilibrium real...
The blue whale (Balaenoptera musculus) is thought to be the largest animal ever to inhabit the Earth. The longest recorded blue whale had a length of 108 ft. What is this length in meters?
What is the problem with an always balanced budget rule?
Which OD techniques would you consider using, and why?p. 477
The financial statements for Fardy Limited are shown below: During the year, the company purchased a capital asset valued at $ 10,000; payment was made by issuing common shares. Additional capital...
Interest expense on a note payable is only recorded at maturity. True or False
Suppose that $f$ is a cubic polynomial. Prove that for $\delta \in \mathbb{R}$, \[f(x+\delta)=f(x)+\delta f^{\prime}(x)+\frac{1}{2} \delta^{2} f^{\prime \prime}(x)+\frac{1}{6} \delta^{3}...
Define a sequence of functions { f n ( x ) } n = 1 { f n ( x ) } n = 1 as f n ( x ) = n 2 x ( 1 x ) n f n ( x ) = n 2 x ( 1 x ) n for x [ 0 , 1 ] x [ 0 , 1 ] . Determine whether \[\lim _{n...
Your friend balances a package with mass m = 10 kg on top of his head while standing. The mass of his upper body is M = 55 kg (about 65% of his total mass). Because the spine is vertical rather than...
Brice Looney owns a small retail ice cream parlor. He is considering expanding the business and has identified two attractive alternatives. One involves purchasing a machine that would enable Mr....
A positively charged particle initially at rest on the ground moves $4.0 \mathrm{~m}$ upward in $2.00 \mathrm{~s}$. If the particle has a chargeto-mass ratio of $10 \mu \mathrm{C} / \mathrm{g}$...
Central States Telecom provides communication services in Iowa, Nebraska, the Dakotas, and Montana. Central States purchased goodwill as part of the acquisition of Sheldon Wireless Company, which had...
Shown below is selected information from the financial records of Merris Corporation as of December 31: Required a. Determine which of the above items will appear on the statement of cash flows and...
Pippa runs a photographic studio specializing in black and white portrait photography. Clients book a one hour studio session and are entitled to receive two large photographs of their choice from...
The following information is from the books of Towl Ball Company for the month of April. Cash Receipts Journal Date Cash Received April 2 .......... $ 2,500 5.................... 2,000...
Define relevant costs and discuss: (1) whether all future costs are relevant for decision making and (2) whether variable costs are always relevant and fixed costs are always irrelevant
You are given the following regression output, where the height of a person, in inches, is being used to predict the amount that person sleeps per night, in hours. What is the equation of the...
Which answer best describes the direction, form, and strength of the association between the distance of a hike (in miles) and the time it takes to complete the hike (in minutes). A. Positive,...
Which answer best describes the direction, form, and strength of the association between physical warmth (Temp) as measured by oral temperature in degrees Celsius and social warmth as measured by a...
On consolidated financial statements, where does the parents equity in the net income of the subsidiary account appear? A. On the consolidated income statement, as a revenue B. On the consolidated...
Which of the following is not one of the elements of the balanced scorecard? a.cost system b.strategic initiatives c.performance targets d.strategy maps
Yield to Maturity and Call with Semiannual Payments Shares Remaining After Recapitalization Dye Trucking raised $75 million in new debt and used this to buy back stock. After the recap, Dye's stock...

Suppose that (f) is a quadratic polynomial. Prove that for (delta in mathbb{R}), [f(x+delta)=f(x)+delta f^{prime}(x)+frac{1}{2} delta^{2} f^{prime

Question:

Step by Step Answer:

The given formula holds true for quadratic polynomials degree 2 because the Taylor Series expansion ...View the full answer

Introduction To Statistical Limit Theory

Students also viewed these Business questions