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