Calculus

1/X by first principles

  1. 0
  2. 0
  3. 12
asked by Kristin
  1. What do you want, the derivative?
    if so
    f(x) = 1/x
    f(x+h) = 1/(x+h)

    f(x+h)-f(x) = 1/(x+h) - 1/x

    = [ x -(x+h)] /[x(x+h)]

    = -h/ (x^2 + x h)

    [f(x+h)-f(x)]/h = -1/(x^2+xh)

    limit as h-->0
    = -1/x^2

    which is of course the derivative

    1. 0
    2. 0
    posted by Damon
  2. Where did -h come from

    1. 0
    2. 0
    posted by Kristin
  3. h is a small increase in x which is allowed to approach zero to get the slope of f(x) at x, the definition of the derivative

    Definition of deriviative of f(x) is:
    df/dx = {f(x+h) - f(x) ]/h as h-->0

    1. 0
    2. 0
    posted by Damon
  4. Oh, if you mean the algebra look at the numerator
    [ x -(x+h)] = x - x - h
    = -h

    1. 0
    2. 0
    posted by Damon

Respond to this Question

First Name

Your Response

Similar Questions

  1. U.S. GOVERNMENT

    George Mason stated: "no free government, or the blessings of liberty can be preserved to any people, but by frequent recurrence to fundamental principles." considering contemporary issues, what are these "fundamental principles"

    asked by I NEED HELP!!!!!!!! on September 1, 2007
  2. english - phrases

    "Stick to your principles". Is to your principles an adjectival or adverbial or verbal phrase? Or none of the above?? Can you please help me turn it into one of the phrases mentioned above. THAAAAANKS :D I don't see an adverb. All

    asked by amanda on August 10, 2006
  3. U.S. History

    Explain four principles on which the Constitution is founded. How does the Constitution incorporate these principles into a plan for government? How do you see these principles at work in government today?

    asked by Anonymous on October 4, 2018
  4. auditing

    I have been asked "Determining whether amounts are in conformity with GAAP addresses the proper measurements of assets, liabilities, revenues, and expenses which includes all of the following except: a. the reasonableness of

    asked by Nick on December 19, 2011
  5. com130

    identify two ethical principles that should guide technical communications. Explain each of the principles you chose and provide an example of why each is important.

    asked by Anonymous on October 29, 2009
  6. psy

    How do the evolutionary principles of “natural selection” and “fitness” help to shape the overall behavior and development of the human species? According to the principles of evolution, what are some behaviors that might

    asked by sam on June 23, 2011
  7. English

    In the book, Language in Thought and Action 5th edition, by S.I and Alan Hayakawa, what are the main principles? I have a few already: 1)Cooperation is essential in order to have a society. 2)Words aren't the only thing associated

    asked by Theo on July 30, 2009
  8. HCA

    a 700- to 1,050-word paper that includes the following: • Describe the principles of verbal and nonverbal communication. • Explain which three principles you think are critical for effective communication. • Include at least

    asked by jackie on October 9, 2012
  9. Accounting

    Scott Brothers, Inc. follows the qualitative characteristic of consistency. This means that Answer a. Scott applies the same accounting principles as its competitors. b. Scott has elected certain accounting principles that can

    asked by Anton on September 23, 2012
  10. ART

    Thanks for the websites, I have a worksheet of a list of all the elements and principles, but i am still struggling as to which elements and which principles apply to this painting "Polly, Minou and Eon" by Will Barnet..any

    asked by Mandy on October 27, 2011
  11. english

    If, . . . my father had taken the pains to explain to me that the principles of Agrippa had been entirely exploded and that . . . the powers of [Agrippa] were chimerical, . . . I should certainly have thrown Agrippa aside. . . A

    asked by Sammy on August 29, 2015

More Similar Questions