Calculus 1A, College of the Desert, Chapters1-4.txt

Card Set Information

Author:
Mattyj1388
ID:
33033
Filename:
Calculus 1A, College of the Desert, Chapters1-4.txt
Updated:
2011-06-23 18:27:33
Tags:
Chapters1 Calculus 1A
Folders:

Description:
general info
Show Answers:

Home > Flashcards > Print Preview

The flashcards below were created by user Mattyj1388 on FreezingBlue Flashcards. What would you like to do?


  1. Lim F(x) = L
    x-->a




    • We say "the limit of F(x), as "x" approaches "a", equals "L".
    • If we can make the values of F(x) arbitrarily close to "L" (as close to "L" as we like) by taking "x" to be sufficiently vlose to "a" ( on either side of "a") but not equal to "a".

    (page 88)
  2. Function
    A function "F" is a rule that assigns to each element "x" in a set "D" exactly one element, called F(x), in a set "E".
  3. Increasing
    F(x1) < F(x2) whenever x1 < x2 in I.

    (page 20)
  4. Decreasing
    F(x1) > F(x2) whenever F(x1) > F(x2) in I.

    (Page 20)
  5. d/dx (sin x) =
    Cos x

    (page 193)
  6. d/dx (cos x) =
    -sin x

    (page 193)
  7. d/dx (tan x) =
    Sec2 x

    (page 193)
  8. d/dx (csc x) =
    -csc x cot x

    (page 193)
  9. d/dx (sec x) =
    Sec x tan x

    (page 193)
  10. d/dx (cot x) =
    -csc2 x

    (page 193)
  11. d/dx (C) =
    0

    (page 187)
  12. d/dx (xn) =
    nxn-1

    Page 187
  13. d/dx (ex) =
    ex

    Page 187
  14. (cf)' =
    cf '

    Page 187
  15. (f+g) ' =
    f ' + g '

    Page 187
  16. (f-g) ' =
    f ' - g '

    Page 187
  17. (fg) ' =
    fg ' + f 'g

    Page 187
  18. (f/g) ' =
    • (gf ' - fg ')
    • g2

    Page 187
  19. Lim sin x/ x =
    X-->0
    1

    Page 190
  20. Lim (cos x -1)/x =
    x-->0
    0

    Page 192
  21. Chain Rule
    • If "g" is differentiable at "x" and "f" is differentiable at g(x), then the composite function F=f • g defined by F(x) = f(g(x)) is differentiable at "x" and F ' is given by the product
    • F '(x) = f '(g(x)) • g '(x)
    • In Leibniz notation' if y = f(u) and u = g(x) are both differentiable functions, then
    • dy/dx = (dy/du)(du/dx)

    Page 197
  22. Power Rule combined with the Chain Rule
    If "n" is any real number and u = g(x) is differentiable, then

    • (d/dx)(un) = (nun-1)(du/dx)
    • Alternatively
    • (d/dx)(g(x))n = n(g(x))n-1 •g '(x)
  23. d/dx(sinh-1(x)) =
    Chapter 3
    1 / ((1+x2)1/2)
  24. d/dx(cosh-1(x)) =
    Chapter 3
    1 / ((x2-1)1/2)
  25. d/dx((tanh-1(x)) =
    Chapter 3
    1 / (1-x2)
  26. d/dx(csch-1(x)) =
    Chapter 3
    -1 / (|x|(x2+1)1/2)
  27. d/dx(sech-1(x)) =
    Chapter 3
    -1 / (x(1-x2)1/2)
  28. d/dx(coth-1(x)) =
    Chapter 3
    1 / (1-x2)
  29. Absolute maximum
    • aka: global maximum
    • A function "F" has an absolute or global maximum at "c" if F(c) >_ F(x) for all x in D, where D is the domain of F. The number F(c) is called the Maximum Value of F on D. Also called an extreme value.
  30. Absalute Minimum
    F has an absalute minimum at "c" if F(c) <_F(x) for all x in D and the number F(c) is called Minimum Value of F on D. Also called an extreme value.
  31. Local Maximum
    A function F has a Local Maximum (or relitive maximum) at "c" if F(c) >_F(x) when x is near c. [This means that F(c) >_ F(x) for all x in some open interval containing c]. Similary, F has a Local Minimum at c if F(c) <_ F(x) when x is near c.
  32. Extreme Value Theorem
    If F is continuouse on a closed interval [a,b], then F attains an absolute maximum value F(c) and an absalute mimimum value F(d) at some numbers c and d in [a,b].

What would you like to do?

Home > Flashcards > Print Preview