Consider the function f(x) = x e x , tabulated below: (a) Find, exactly, f(1) and f(1).

Question:

Consider the function f(x) = x e^x, tabulated below:

X 0.96 0.97 0.98 0.99 1.00 f(x) 2.5072 2.5588 2.6112 2.6643 2.7183 x 1.01 1.02 1.03 f(x) 2.7731 2.8287 2.8851

(a) Find, exactly, f´(1) and f"(1).

(b) Use the tabulated values and the formula

to estimate f´(1), for various h. Compute the errors involved and comment on the results.

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

Step by Step Answer:

Related Book For book-img-for-question

Modern Engineering Mathematics

ISBN: 9781292253497

6th Edition

Authors: Glyn James

See More Books

Question Posted: Jan 13, 2024 09:05 AM

See More Questions

a. Example 13-1: Batch Reactor with an Exothermic Reaction Wolfram 1. Adiabatic Case: Use Wolfram to see whether you can find a trajectory that is ready to ignite and whose trajectory looks like a...
Consider the function f (x) = 3(x + 1)2 - 4. a. Find f (5). b. Find f (n). c. Find f (x + 2). d. Use your calculator to graph y = f (x) and y = f (x + 2) on the same axes. How do the graphs compare?
Consider the function f (x) = sin4 x + cos4 x (a) Use the power-reducing formulas to write the function in terms of cosine to the first power. (b) Determine another way of rewriting the original...
In Problems, assume that the populations are normally distributed and that independent sampling occurred. (a) Test the hypothesis that 1 2 at the a = 0.1 level of significance for the given sample...
Crew members attempt to escape from a damaged submarine 100 m below the surface. What force must be applied to a pop-out hatch, which is 1.2m by 0.60 m, to push it out at that depth? Assume that the...
A 200-g aluminum calorimeter contains 500 g of water at 20oC. Aluminum shot of mass 300 g is heated to 100oC and is then placed in the calorimeter. (a) Using the value of the specific heat of...
Describe the hiring decision of a perfectly discriminating monopsonist and of a nondiscriminating monopsonist. In what sense do monopsonists exploit workers?
Nutritional Foods reports merchandise inventory at the lower-of-cost-or-market. Prior to releasing its financial statements for the year ended March 31, 2017, Nutritionals preliminary income...
Tarrant Amertex Regional Hospital, one of our hospitals in the Fort Worth area, has been in need of a new Chief Executive Officer. Last week, we reached a "handshake" dealthough per current protocols...
Use the following table of f(x) = (ex e x )/2 to estimate f'(1.0) by means of an extrapolation method. Compare your answer with (e + e 1 )/2 = 1.5431 correct to 4dp. 0.2 f(x) 0.2013 0.6 0.8 0.6367...
Use your calculator (in radian mode) to calculate the quotient {f(x + h) f(x h)}/(2h) for f(x) = sin x, where x = 0(0.1)1.0 and h = 0.001. Compare your answers with cos x.
What artifacts, rituals, language/jargon, and narratives/stories have you observed in your workplace?
Design a vertical shell and tube condenser for the duty given in question 12.7. Use the same preferred tube size. Data from 12.7 A condenser is required to condense n-propanol vapor leaving the top...
A $0.2-\mathrm{kg}$ cart 1 initially at rest is struck by an identical cart 2 traveling at $v_{2 x, i}=+0.5 \mathrm{~m} / \mathrm{s}$ along a low-friction track. After the collision, the velocity...
The data in the table were recorded for two race cars, A and $B$, driving down a straight stretch of track. Determine the average velocity of car B as measured by an observer in car A. Time (s) Car...
Ethanol(1) + benzene(2) form azeotropic mixtures. Compare the specified model to the experimental data of Brown and Smith cited in problem 10.2. (a) Prepare a y-x and P-x-y diagram for the system at...
Name two example embedded systems that implement a DOS-compatible file system.
What are the three reasons firms use budgets?
Ex. (17): the vector field F = x i-zj + yz k is defined over the volume of the cuboid given by 0x a,0 y b, 0zc, enclosing the surface S. Evaluate the surface integral ff, F. ds?
The reaction of atomic chlorine with ozone is the first step in the catalytic decomposition of stratospheric ozone by Cl . Cl (g) + O 3 (g) ClO (g) + O 2 (g) At 298 K the rate constant for this...
In addition to Cl , other halogens can potentially contribute to stratospheric ozone loss. For example, consider the reaction of Br with ozone: Br (g) + O 3 (g) BrO (g) + O 2 (g) At 298 K the rate...
A standard rule of thumb for thermally activated reactions is that the reaction rate doubles for every 10 K increase in temperature. Is this statement true independent of the activation energy...
During Morch, manufacturing company produced 6,000 ott and has the following manufacturing costs: valable costs $31 per unit, find conto $22 per unit. The factory monthly production capacity is...
An investment firmandes 5,900 accounts. The accounts can be broken down into business operos, dan terken down by investment strategy for core See the tablete Business Personal Total 3.155 915...
The cash savings from reduced dividend payments resulting from a stock repurchase strategy can allow the company to increase its dividends for remaining shareholders. Explain

Consider the function f(x) = x e x , tabulated below: (a) Find, exactly, f(1) and f(1).

Question:

X 0.96 0.97 0.98 0.99 1.00 f(x) 2.5072 2.5588 2.6112 2.6643 2.7183 x 1.01 1.02 1.03 f(x) 2.7731 2.8287 2.8851 1.04 2.9424

Step by Step Answer:

Taking h 004 fxxe fxe xe e1 x fx e1x e e 2 x so f1 2e f1 f104 096 008 ...View the full answer

Modern Engineering Mathematics

Students also viewed these Sciences questions