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 answer-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?
Two long, parallel conductors carry currents in the same direction as shown in Figure P30.63. Conductor A carries a current of 150 A and is held firmly in position. Conductor B carries a current IB...
When conducting an incremental analysis, what step must always be taken immediately prior to beginning the pairwise comparisons? a. Order the alternatives from highest to lowest initial investment b....
Special Order Louisville Corporation produces baseball bats for kids that it sells for $32 each. At capacity, the company can produce 50,000 bats a year. The costs of producing and selling 50,000...
Using financial statements for each of ROSS STORES and SUNOCO, which are provided to you on CANVAS: for the main year of reporting and the immediate preceding year, and using the latest version of...
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...
Bad debt expense is estimated using the percentage-of-sales method. Total sales for the year were $600,000. The ending balance in Accounts Receivable was $100,000. Historically, bad debts have been...
The speed of a flywheel changes from 10 rad/s to 30 rad/s in 5 seconds time. Determine the angular acceleration of the wheel. How many revolutions the wheel would turn to attain a speed of 600...
An ambulance is generating a siren sound at a frequency of 2,400 Hz. The speed of sound is 345.0 m/s. If the observer is traveling at a velocity of 24.00 m/s toward the stationary ambulance, then...
A circular coil of wire has 35 turns of wire each with a radius of 20 cm. The circular coil rotates with an angular velocity of 35 rotations per second. The circular coil has a net resistance of 0.25...
10) An athlete is standing unclothed in a locker room whose dark walls are at some temperature. The rate of heat flow by radiation is 150 W. Estimate the temperature of the walls assuming a skin...
A moose trots past a light post located 13 m to the right of the Shore Ave signpost. It then passes another light post located 23 m to the left of the same Shore Ave sign 12 s later. What is the...
Why is light sometimes described as rays and sometimes as waves?
Shreemaya Hotel in !adore was facing a problem of low demand for its rooms due to off season. The Managing Director (MD) of the hotel, Mrs. Sakina was very worried. She called upon the Marketing...
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...
Required information [The following information applies to the questions displayed below.] Laker Company reported the following January purchases and sales data for its only product. For specific...
Use the price-demand equation to find the values of p for which demand is elastic and the values for which demand is inelastic. Assume that price and demand are both positive. x=f(p)=3174-6p2 The...
Vinti operainy expenses Interest income Interest expense Net income Consolidated net income 51,000 UJ, JUU (25,200) 0 0 40,500 $ (162,950) $ (34,500) 0 $ 0 to noncontrolling interest to Pikes $ 0...

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:

Introduction To Statistical Limit Theory

Students also viewed these Business questions