(a) Show that ex 1 x for x 0 (b) Deduce that ex 1 x frac12 x2 for x 0 (c) Use mathematical induction to prove that for x 0 and any positive integer n, e 1 x 2 n ...

a Let fx e1r Now f0 e 1 0 and for z 20 we have fx e 1 0 No ...

(a) Show that ex > 1 + x for x > 0. (b) Deduce that ex >...

Question:

(a) Show that ex > 1 + x for x > 0.
(b) Deduce that ex > 1 + x ½ x2 for x > 0.
(c) Use mathematical induction to prove that for x > 0 and any positive integer n,

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

Step by Step Answer:

Related Book For book-img-for-question

College Algebra Graphs and Models

ISBN: 978-0321845405

5th edition

Authors: Marvin L. Bittinger, Judith A. Beecher, David J. Ellenbogen, Judith A. Penna

See More Books

Question Posted: Jun 30, 2010 01:59 AM

See More Questions

Use mathematical induction to prove that for n > 2, ..+ an-12"-1 +1") det(C, A1) = (-1)"(o + ajd + = (-1)" p(2)
Use mathematical induction to prove that if n people stand in a line, where n is a positive integer, and if the first person in the line is a woman and the last person in line is a man, then...
Use mathematical induction to prove each of the following. a. b. c. The sum of n terms of an arithmetic sequence: a1 + (a1 + d) + (a1 + 2d) + ....... + [a1 + (n - 1) d] = n / 2 [2a1 + (n - 1)d) (i t-...
What is Monetary system? Presentation Introduction, definition, examples, advantages, disadvantage, conclusion
Gary Brown Manufacturing makes single kayaks, double kayaks, and lightweight competitive kayaks. The double kayak line has been showing losses for several years, and management is considering...
A sample of n = 7 scores has a mean of M = 5. After one new score is added to the sample, the new mean is found to be M = 6. What is the value of the new score? (Hint: Compare the values for X before...
Refer to the information in QS 6-8 and assume the perpetual inventory system is used. Determine the costs assigned to ending inventory when costs are assigned based on the weighted average method....
Two light sources of identical strength are placed 10 m apart. An object is to be placed at a point P on a line parallel to the line joining the light sources and at a distance d meters from it (see...
Total fixed costs for Green Planes Inc. are $120,000. Total costs, including both fixed and variable, are $400,000 if 180,000 units are produced. The total variable costs at a level of 260,000 units...
Tyler, a self-employed taxpayer, travels from Denver to Miami primarily on business. He spends five days conducting business and two days sightseeing. His expenses are $400 (airfare), $150 per day...
Show that tan x > x for 0 < x
Show that a cubic function (a third-degree polynomial) always has exactly one point of inflection. If its graph has three x-intercepts x1, x2 and x3, show that the -coordinate of the inflection point...
The balance in the supplies account, before adjustment at the end of the year, is $9,000. Journalize the adjusting entry required if the amount of supplies on hand at the end of the year is $1,575.
A new partner C is invited to join in the AB partnership. Currently, A's and B's capital are $540,000 and $100,000, respectively. According to their profit and loss sharing contract, partner A and B...
The two tanks shown are connect through a mercury manometer. What is the relation between ???? and ? water Az water Ah
1. After reading about the types of rights that prisoners have while incarcerated, which of these rights, if any, should be reduced or diminished? Why? 2. In the same way, what rights do you believe...
According to the Socratic view of morality summarized by Frankena, is a person brought up by immoral parents in a corrupt society capable of making correct moral judgements? Why or why not? Do you...
Loma Company manufactures basketball backboards. The following information pertains to the company's normal operations per month: Output units15,000 boards Machine-hours4,000 hours Direct...
What are the reasons that private insurers have not been interested in providing coverage against risks such as floods? Why can the federal government offer protection against this risk? Note:...
-x/2 x/4 If A = -x/2 and A-1 =6 then x equals
Evaluate lim arcsin| x1 1-x 1 - X
(a) Approximate f by a Taylor polynomial with degree n at the number a. (b) Use Taylor's Inequality to estimate the accuracy of the approximation f(x) T n (x) when x line in the given interval. (c)...
(a) Approximate f by a Taylor polynomial with degree n at the number a. (b) Use Taylor's Inequality to estimate the accuracy of the approximation f(x) T n (x) when x line in the given interval. (c)...
(a) Approximate f by a Taylor polynomial with degree n at the number a. (b) Use Taylor's Inequality to estimate the accuracy of the approximation f(x) T n (x) when x line in the given interval. (c)...
Callaho Inc. began operations on January 1 , 2 0 1 8 . Its adjusted trial balance at December 3 1 , 2 0 1 9 and 2 0 2 0 is shown below. Other information regarding Callaho Inc. and its activities...
Required: 1. Complete the following: a. Colnpute the unit product cost under absorption costing. b. What is the company's absorption costing net operating income (loss) for the quarter? c. Reconcile...
Bond Valuation with Semiannual Payments Renfro Rentals has issued bonds that have an 8% coupon rate, payable semiannually. The bonds mature in 6 years, have a face value of $1,000, and a yield to...

(a) Show that ex > 1 + x for x > 0. (b) Deduce that ex >...

Question:

e*>1+x++ 2! n!

Step by Step Answer:

a Let fx e1r Now f0 e 1 0 and for z 20 we have fx e 1 0 No...View the full answer

College Algebra Graphs and Models

Students also viewed these Calculus questions