MTH 122 Exam 1 Practice

Card Set Information

Author:
Jdean84
ID:
258759
Filename:
MTH 122 Exam 1 Practice
Updated:
2014-01-29 16:42:03
Tags:
Math
Folders:

Description:
Calculus for social sciences
Show Answers:

Home > Flashcards > Print Preview

The flashcards below were created by user Jdean84 on FreezingBlue Flashcards. What would you like to do?


  1. Definition: Limit of a Function
    • The function f has the limit L as x approaches the number a, written
    •  
    •    lim f(x) = L
    •    x->a

    if the value of f(x) can be made as close to the number L as we please by taking x sufficiently close to (but not equal to) the number a
  2. Right-handed limit of a function
    • lim f(x) = L
    •   x->a+

    Limit as x approaches a from the right
  3. Left-handed limit of a function
    • lim f(x) = L
    •    x->a-

    Limit as x approaches a from the left
  4. Limits at infinity
    • lim f(x)
    • x->
  5. a non-zero number
               0
    = infinity
  6. the Intermediate value theorm
    If f is a continuous function on a closed interval [a,b] and M is any number between f(a) and f(b) then there is at least one number 'c' in [a,b] such that f(c)=M
  7. Existence of Zeros in a continuous function
    If f is a continuous function on a closed interval [a,b], and if f(a) and f(b) have opposite signs, then there is at least 1 solution of the equation f(x)=0 in the interval [a,b]
  8. Secant line
    Passes through at least 2 points on a curve
  9. Tangent Line
    a straight line that "just touches" the curve at a given point
  10. slope of a secant line
    • M= Δy
    •      Δx

    • =f(x+h)-f(x)
    •          h
  11. Slope of a Tangent Line
    • lim   f(x+h)-f(x)
    • h→0        h
  12. Determine the equation of the tangent line of f(x)=x2-2x+1 at the point (0,1)
    • A. Find Derivative: f'(x)=2x-2
    • B. Determine slope of tan line (M) at the point (0,1): f'(0)=-2
    • C. determine equation of tan line at the point(0,1):    y-y1=M(x-x1) M=-2, x1=0, y1=1 y=-2x+1
  13. Average Rate of Change
    • Slope of the Secant Line
    • f(x+h)-f(x)
    •       h
  14. Instantaneous Rate of Change
    • Slope of the tangent line
    • lim     f(x+h)-f(x)
    • h->0        h
  15. Product Rule
    (fg)'=f · g' + g · f'
  16. Quotient Rule
    • f(x)  = g(x) · f'(x) - f(x) · g'(x)
    • g(x)             [g(x)]2

What would you like to do?

Home > Flashcards > Print Preview